WinBack: Covert Operations on the PS2 is an update of a Nintendo 64 game of the same name- a third-person cover-based shooter, but one from 1999. It improves the graphics and adds mediocre Japanese voice acting and awful English voice acting.
It's apparently set in a world where the ability to jump is nonexistent. At least, that's what the architecture and traps imply.
It's not a horror game, but the black guy dies first. Like a chump.
Your main character is named Jean-Luc Cougar. Another teammate is named Keith Birdy. There are (sadly) no animal puns in this game.
When they tell you that you have three hours before a giant space laser attacks your beloved country of America (a second time, the first shot happens in the intro), they're not kidding. That said, the plot twist that happens if you meet this time limit seems tenuously related to how good of a secret agent you are.
If you try to turn out of cover when you're more than a step away from the edge, you do a big sweeping turn into what can only be described as a power stance. If you use the lock-on feature, you can actually do this without being shot to pieces and looking like an asshole. That said, it's totally useless. I love it.
The different guns are less like a selection of toys and more like tools for different jobs (except the silenced pistol, unless you consider "being awful" a job). It's an approach I miss, though even here it can be a drag for 30 stages.
If you have a PS2, you should get it and play it (on easy, the checkpointing is god awful). Then use these nifty unlock codes to mess around with the different modes. I recommend Sudden Death, as it takes a silly amount of bullets to put people down sometimes. Since this is one of those games where enemies react to individual bullets as if being shot is actually uncomfortable, there are more than a few cases of "AUGH-UGH-AUGH-OOH-AUGH-URRrrrrrh."
The game looks like this:
Power stance here at the 22 second mark:
Have time? Play game.