Not that one either :D

Matrix: Path of Neo?

Not Matrix: Path of Neo, but it's warmer, kind of :D

Enter the Matrix then? (No idea - I've never played it)

Enter the Matrix is colder than Half Life: Blue Shift, Matrix: Path of Neo is warmest yet.
It isn't anything Matrix, though, even if one of the hints is. Figure out my devilish riddle! :D

An additional picture too. It's been a while since I played it and I'm having trouble finding good pictures so the uniform might be... inspired. That is to say it could be completely wrong :D

/edit: This game should've been way more popular than it was.
Here's a new picture that probably won't help at all :D
One of the pictures I've posted is a name hint :)
I've also hidden subliminal hints all over the place.

Project Snowblind, maybe?

If the last picture is a name hint, the game is probably taking place on the moon. Not that I have a clue what it could be.

Johnny Mnemonic the video game?

Not Project Snowblind or Johnny Mnemonic the video game.

Here's another name hint.
The left one is missing one letter.
The right one has one letter too many.
:D

Tokyo Cat? ... Hm, no. I can't construct the name of a game I know from that by removing a letter and adding another one.

Not Tokyo Cat, but the idea is right, and all the necessary words have been used in guesses thus far. :D

That wouldn't make sense, that would make the game Half-Life 2 since NeoTokyo is just a mod.

It would make sense assuming that full conversions count as games. Yeah, it's controversial but whatever. :P
I was actually close to guessing "The Specialists" for a minute (another Half-Life (1) mod).

NEOTOKYO is correct, your turn :)

As I see it, full conversion mods like NEOTOKYO, Counter-Strike, etc. are games, but I would've taken Half Life 2 as an answer too. :p