I didn't know that there was a fan remake of Timesplitters in the works. That's pretty cool actually, I'm definitely keeping my eye on this. My old roommates and I played the shit out of TS2 and TSFP.
Me and my uncle used to play Timesplitters 2 every day, God that shit was great fun, AND IT HAD A REAL ACHIEVEMENT SYSTEM.
Seriously, it was MADE for multiplayer and had a excellent singleplayer yet............no PC release where it would of really shined .
THE BEST METHOD to run PSX games (and everything else for that matter) is via Retroarch - http://buildbot.libretro.com/nightly/
If you have any questions on how to set it up on Windows please feel free to ask, its very easy.