You can put someone in check, so you should be able to put someone in checkmate. The opponent is in a state where he is checkmated, and you have played the move that put him in that state of checkmate. I don't see a problem here.
Put him in checkmate!
I agree with Tenna. Check is a state which you can pass through and thus be "in". Checkmate is final and thus you can't be "in checkmate", the word merely describes the state of things.
There's also no conceivable reason you would say "put [X] in checkmate" rather than "checkmate." or "checkmated him"
Also, there are only 329 Google hits for "put in checkmate."

Like I said, if checkmate is a state of things, and you caused your opponent to be in that state, you have put him in checkmate. I am not saying it is more reasonable or popular than other phrases, but I am saying that it is unreasonable to want to commit violent acts on people who utter a perfectly plausible phrase.

Well, I don't like "I put him in check" either. I don't see it as the a person putting another person in check, but rather a move putting a person in check. So "Ne6 is illegal because it would put him in check" is fine, but "if he goes there then I'll put him in check with Bh4" isn't.
Besides, you can't ever be "in checkmate". Once there's checkmate, you're no longer playing the game!

Pretty sure checkmate is a noun, ergo you can put someone into checkmate.
Using it as a verb insinuates that the shortened version 'mate' can also be used as a verb in a similar context. This obviously invites one to be 'mated' by ones opponent. As we all know, chess players are very seldom mated (by their opponent or anyone else for that matter) - thus indicating that the usage as a verb is contradictory to reality.

Surprised that it gets to you so much. A kid hollering "check!" in an adult tournament grinds most people's gears, but didn't know that not using the word checkmate correctly indicated a lack of respect for/knowledge of the game.

Statements like "It is illegal to play a move would place your king in check" are pretty common, and even cited in the rules, and would seem to imply that the noun is valid. We're also often reminded to keep an eye out for our opponent's checks and the potential consequences (forks, moving with tempo etc.).
To check someone's king, or checkmate someone are in such common usage, though, that it's hard to imagine that the verb is also not acceptable. That said, in colloquial speech it's not uncommon to just verbacize a noun like that, so perhaps it's not.

Pretty sure checkmate is a noun, ergo you can put someone into checkmate.
Titanium is also a noun, but can you put someone into titanium?

Surprised that it gets to you so much. A kid hollering "check!" in an adult tournament grinds most people's gears, but didn't know that not using the word checkmate correctly indicated a lack of respect for/knowledge of the game.
But the thing is, I wouldn't care if the kid yelled "check!" (or for that matter, I'M GONNA CHECKMATE YOUR ASS SO BAD" after every move) as long as that's how he said it...

Pretty sure checkmate is a noun, ergo you can put someone into checkmate.
Titanium is also a noun, but can you put someone into titanium?
If it's molten, yes.

Well, I don't like "I put him in check" either. I don't see it as the a person putting another person in check, but rather a move putting a person in check. So "Ne6 is illegal because it would put him in check" is fine, but "if he goes there then I'll put him in check with Bh4" isn't.
Now it sounds like you just want the rest of the planet to adhere to your idiosyncracies. Personally I don't like the past tense verb form, "checkmated," but I deal with it because people can say what they want to.

I agree with Tenna. Check is a state which you can pass through and thus be "in". Checkmate is final and thus you can't be "in checkmate", the word merely describes the state of things.
There's also no conceivable reason you would say "put [X] in checkmate" rather than "checkmate." or "checkmated him"
Also, there are only 329 Google hits for "put in checkmate."
right now there are about 543,000 hits for put in checkmate
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has 2 hits used to have only one hit

Pretty sure checkmate is a noun, ergo you can put someone into checkmate.
Titanium is also a noun, but can you put someone into titanium?
If it's molten, yes.
peace is a noun can you put someone in peace?

I agree with Tenna. Check is a state which you can pass through and thus be "in". Checkmate is final and thus you can't be "in checkmate", the word merely describes the state of things.
There's also no conceivable reason you would say "put [X] in checkmate" rather than "checkmate." or "checkmated him"
Also, there are only 329 Google hits for "put in checkmate."
Being in something doesn't mean there has to be a way out.
Okay, so I've been wondering this for a while.
Does it annoy anyone else when people say "put him in checkmate"? I've always preferred "checkmate him" . When people say "put him in checkmate" I always want to just strangle the person saying it and tell him to shut up, since he obviously has no idea what he's talking about. There are a few other phrases that are like this, but none irks me as much as "put in checkmate".
It's not like there are any general-use idioms in the English language that peeve me to this extent. It's just "put in checkmate". Something sounds so wrong and ignorant about it. It's like anyone who says that should be slapped across the face or something.