Is having a high IQ necessary to become World Champion in chess like Magnus Carlsen?

most IQ tests I take show between 145-163, I passed the paid MENSA test mostly out of curiosity, not because I wanted to join. Yet in chess I am struggling to improve. I started chess a few months ago thinking if I can learn new computer languages and how to design circuit boards quickly and easily, then mastering chess should not be a problem. I was very wrong. Chess has tried my patience like nothing else I have ever tried to learn. one would think a math and engineering background would predispose someone to being a natural at chess, yet I have not found this the case. I have eaten a lot of humble pie trying to learn this game, but I think that is actually helping me grow as a person. Because learning always came easily to me , I never developed a great deal of patience and resolve when things got difficult. I've come to realize IQ tests don't mean crap- I know people who couldn't solve a basic math equation or word puzzle who are way more successful than me in life. Life is too complex for a simple number to describe your ability, just like a chess board.
Becoming a great at everything is really hard and challenging. I remember me in the back days thinking that I'm a math genius because I won the math Olympiad between our local district's schools. But after that went further to the my city math Olympiad and I solved only 1 of the 7 potential tasks. You know some people are saying that chess is easy, but they didn't really go deep enough to understand how complicated the game is. So if you will study chess all day long may be you'll have a chance to become a strong GM, not sure about World Champion.

I do not believe the numeric rankings of IQ above 150.
Show me a room full of doctors and I will show you a room full of people with IQ's around 130.
I am pretty sure there is a relationship between pattern finding IQ tests and playing chess.
The game of chess has a lot of simple counting. If material is attacked twice but defended once it is at risk.

I think one of the misleading things that gets people hope up or builds their expectations too high is starting chess on the internet. As a brand new player you are instantly in the same realm mingling on the same forums and watching games of the greatest players. Before the internet, you would play at home and become better than your brother, then see if you could be the best at your school, then it was the coffee shop or library in your town- if you could be the best there you might go play in a club or regional tournament... it was a gradual progression.
Now a new player using an app or website is bombarded with access to GM games and livestreams the second they log in, it can be quite addictive and set false expectations. You see these celebrity GMs livestreaming, but you don't see the countless hours they had their nose in a book or the weekends they spent sitting by themselves over a chessboard.
I think one of the misleading things that gets people hope up or builds their expectations too high is starting chess on the internet. As a brand new player you are instantly in the same realm mingling on the same forums and watching games of the greatest players. Before the internet, you would play at home and become better than your brother, then see if you could be the best at your school, then it was the coffee shop or library in your town- if you could be the best there you might go play in a club or regional tournament... it was a gradual progression.
Now a new player using an app or website is bombarded with access to GM games and livestreams the second they log in, it can be quite addictive and set false expectations. You see these celebrity GMs livestreaming, but you don't see the countless hours they had their nose in a book or the weekends they spent sitting by themselves over a chessboard.
That's 100% correct - nothing I can add.

I do not believe the numeric rankings of IQ above 150.
Show me a room full of doctors and I will show you a room full of people with IQ's around 130.
I am pretty sure there is a relationship between pattern finding IQ tests and playing chess.
The game of chess has a lot of simple counting. If material is attacked twice but defended once it is at risk.
I think chess requires some attributes beyond raw intellectual horsepower- it requires conciencess and precision. Vasily Ivanchuk has had probably the most brilliant games ever in the history of chess at linares in '91 I think it wss, he has proven he had the raw ability to be world chess champion in his beautiful mate of Kasparov, but he lacked the consistency and precision.
Even the most brilliant chess play can fall to one simple mistake or oversight- like a picasso with a hole in the canvas. Sometimes getting excited about a genius attack will cause you to miss your opponents threat. There are multiple aspects of playing well - precision, patience, consistency, etc... without these traits even the most intellectual player will fall...
Yeah, tactical vision and good memory are really important parts of the success over the chess board. AndBell, did you see some kids with >2200 rating? They have high rating not because they are smart but because they trained their tactical vision a lot and memorized many opening variations. If they will face a mediocre adult with 2000 rating they are going to lose. Their FIDE rating is mostly based on technique not on genius but there are also some exceptions. Anyway exceptions prove the rule
High spatial recognition reasoning and strong memory.
That's not enough to become a World Champ. Great intelligence is required for it.

I think bullet & blitz play is a whole different set of skills as well- very fast pattern recognition, reaction time, etc... I often think if Hikaru played something else like starcraft II for example he would probably be a beast at it. His puzzlerush is amazing
Not really. Blitz requires the same abilities like a classic game but you're of course limited in the time and here is the difference: you need to know a lot of theory to be good at blitz to make decisions as fast as possible. But in a classic game you have more time to think and more opportunities to be creative.
I mean you can't let your king walk to f8 or d6 squares (playing Black) in the opening if you have a blitz game because it will be really dangerous for you but if you're playing classic game you might try some contradictory variations.

most IQ tests I take show between 145-163, I passed the paid MENSA test mostly out of curiosity, not because I wanted to join. Yet in chess I am struggling to improve...
Me too. I got 157 on the Mensa test and I know many of the things needed to be a strong chess player and coached a very successful high school chess team, but I've never been close to being a chessmaster.
You also need to have a good memory for tactics patterns. When GM Yasser Seirawan reported on the 1992 Fischer-Spassky rematch, he said Fischer "can feel where it hurts" the other player. That's a combination of pattern recognition and positional understanding more than calculation. Another GM, asked how far ahead GM's usually think aheadf, answered, "a couple moves." Again, that's because those couple moves reach a position or begin a pattern of moves that the GM knows.
Personally, I have a little "tunnel vision." Psychologists do tests where they put people is a dark room, turn on the light for several seconds, then ask the people what they saw on the wall. People with broad vision will remark there was a clock, a painting, a photograph, moulding where the wall joins the ceiling, etc. but didn't have time to notice details about each one People wilth tunnel vision, might only remember seeing the clock and the painting and remember the clock showed it was 6 o'clock and the painting was a portrait of a woman.
Unfortunately, I have tunnel vision. For example, new restaurant may open on a highway I frequently travel and six months later someone will mention it and I didn't know it was there: it wasn't what I was interested in on that road. Can you see how that's bad for chess? Maybe that's why I dropped a rook in a recent daily game!
To be good a chess, I think you have to have - or at least develop for chess - broad vision. Seeing tactics and positional patterns helps with that. If you recognize a double attack, the ability to pin a piece to an empty square, that a certain square would make a powerful 6th rank Knight Outpost, that if you castle on the opposite side from your opponent your Pawn Storm will get to his King before his Pawns will get to yours, etc. etc. it greatly simplifies things.
So I don't think it requires a high genius level of intelligence to be World Champ, but it requires broad spatial recognition and an excellent memory that allows a deep understanding of tactics and positions and calculation.
That "So I don't think it requires a high genius level of intelligence to be World Champ" thing made me laughing. Take a look at this famous combination before saying such disrespectful words:
Yeah! That's a couple of moves combination! You're right!!!

I don't think Kasparov saw the whole line from 24 till 39 right up till he take Topalov's queen and rook, but improvised as the moves progressed. The position played itself move by move.
When Chessbase Interviewed Magnus
Interview by Maik Grossekathöfer
SPIEGEL: Mr Carlsen, what is your IQ?
Carlsen: I have no idea. I wouldn’t want to know it anyway. It might turn out to be a nasty surprise.
SPIEGEL: Why? You are 19 years old and ranked the number one chess player in the world. You must be incredibly clever.
Carlsen: And that’s precisely what would be terrible. Of course it is important for a chess player to be able to concentrate well, but being too intelligent can also be a burden. It can get in your way. I am convinced that the reason the Englishman John Nunn never became world champion is that he is too clever for that.
SPIEGEL: How that?
Carlsen: At the age of 15, Nunn started studying mathematics in Oxford; he was the youngest student in the last 500 years, and at 23 he did a PhD in algebraic topology. He has so incredibly much in his head. Simply too much. His enormous powers of understanding and his constant thirst for knowledge distracted him from chess.
SPIEGEL: Things are different in your case?
Carlsen: Right. I am a totally normal guy. My father is considerably more intelligent than I am.
I have set my sights on becoming a world chess champion, probably the best ever (not trolling). However, I feel that my IQ may be low than needed to become a champ. I heard that Kasparov's IQ was 135 (before, 187) and Fischer's IQ was around 180. There have been rumors that Carlsen's IQ is around 185. I don't know what my IQ is but I feel that it could be average, unfortunately. I literally can't get this statement out of my head: "You can't become champ without being genius", and it is driving me insane. Maybe I have not fully recognized my potential. I am befuddled.