Looking for help in understanding why the engine thinks this pawn move was a mistake

So basically you're saying it's a mistake because the move was passive to a fault?

I guess can see this since the E4 and C4 pawns did not actually need a d3 defender and with my position, if 8. d4 9. c5xd4 10. Nxd4, 11. regardless of Nxd4 or queen trade, end the result would be fine for me. If black doesn't c5xd4, while I'm not sure how the game will play out it should also be fine...

In addition, my development is mostly done with moving the d4 pawn. I mean a1 rook is not in the game but every other piece is doing something.

Thank you for your time and perspective.

Ah yes the Nb5 move. That was actually one of my favorite moves during this match. On move 10, black moves his queen to d4 and then I play Nb5, attacking the queen and threatening the fork. 

I did not see h3 at all, I agree that would be an interesting move to chase the queen into a useless confined position.

So like ajl721x said, you're saying d3 is passive to a fault.

Thank you for your time and perspective.

I disagree with Optimissed assessment here.  You can learn something from this recommendation, but you must put in some effort to understand why the 8. e5 is so strong (which means you may need to play around with some moves to understand what happens).

For example:

The d3 move you played is not bad - it still leaves you with a strong advantage and you reach the Botvinnik setup you were apparently aiming for.  The reason it is marked as a mistake is that you had a much stronger move you could have made.  The key to learning from engine analysis is to "find the why".  In most cases, the engine is going to point out an obvious tactical shot you missed.  In this case, it is pointing out that you had a way to reach a positionally won game by taking advantage of the fact that you had much better development and piece mobility.  The other lesson you should take from this:  do not play the opening on auto-pilot.  Just because you want a specific setup does not mean you should ignore what your opponent is doing along the way.  Often, you will find a stronger move because your opponent made a mistake in the opening.

A truly appalling game.

d3 wasn't a mistake.

What search depth are you using? At 32 ply, the engine evaluates it as best move.

To play e5, yes, you must understand what is going on.  Perhaps I was wrong, but I did not think the question was "why wouldn't I see this?", but "why is this better than the move I played?"  And that is where I disagree.  When analyzing the game afterwards, taking a look at what happens after e5 is very instructive, especially if you think about how you would reply as Black and see why all those moves fail.  I do agree that if you just look at the engine's top analysis and say "oh, that was a mistake, I should play e5 here" without trying to understand why, it is unhelpful, but like I said, this is a nice instructional position for demonstrating a positional pawn sacrifice.

Not sure which engine you are using, but SF13 gives the following moves (in order of strongest to weakest at depth 35):

1. 8. e5 (+98=2-0)
2. 8. Nb5 (+98=2-0)
3. 8. d4 (+97=3-0)
4. 8. h3 (+92=8-0)
5. 8. d3 (+84=16-0)

SF12 swaps #1 and #2, but all other evals are the same.  Note that all of these moves leave White with a strong advantage, so "mistake" is a bit harsh - 8. d3 just isn't "as winning" as the other choices.

This is my "A truly appalling game" meme:

I am actually not familiar at all with the Botvinnik setup. My knowledge about openings are quite limited. Basically, I know some opening theory, take the middle etc. I've also spent time studying Roy Lopez and a little bit of time looking at the Sicilian. 

When black played e6, I believed the intent was d5 or f5. From previous games and the site's lesson I happen to know the first few moves of the French Defense with d5. So I decided to play c4.

When I was making that decision I already knew my light squared bishop would be blocked in a little and decided I'll make a little outpost for it.

As for playing d3, the primary intent was to open the diagonal for the black squared bishop. I moved to d3 because it did that in addition added a defender to the c4 and e4 pawns. At the time I didn't think d4 was a great move because I had already played c4 and e4. Of course I was wrong in judgement and there's some things for me to learn there.

So I wasn't actually auto-piloting. I only ended with a Botvinnik setup by reacting to what Black played.

While knowing opening would be great, I believe it's more important for me to learn tactics and how to read positions. By read I mean understanding what the position is aiming for and how can I respond to it.

On the topic of "The key to learning from engine analysis is to "find the why"." Definitely agree here.

"8. e5 is so strong"

It seems there is a lot to go through on this. I'll being taking a look at it now.

With that said, thank you for your time and perspective. 

The engine is literally telling you why it considers your move a mistake! When the computer calls one of your moves a "mistake," it's a common error to keep asking "what's wrong with my move?" Most of the time there is nothing wrong with your move, but there was a much better one available! That's where your mistake is. Instead of looking at your move, try to follow the variation the computer is telling you was much better. You will learn a lot more that way

The fact is, White has a terrific position after Black's 7th move, so several moves are just fine. 8.d3 is only a "mistake" in the sense that there were stronger moves. 8.e5, 8.Nb5, and 8.h3 all seem a bit better. But "mistake" seems a bit harsh!

The pawn move is a mistake because it loses an important initiative you had. It therefore dramatically changes the evaluation in your opponent's favor, making it. a mistake