Sorry bro, it isn't that good. It is also a gimmick game, though arguably a better one. Timesplitter's value comes from the sheer amount of game styles (challenge modes of many kinds, level editor, singeplayer and coop, competitive multiplayer). There is a lot of variety on offer, a grabbag of content. However, take any individual aspect alone and it's quite shit, especially the campaign.
It is also from the rareware breed of decline FPS with awful aiming mechanics, flat-plane static overly linear level design, no jumping and crouching, the same one enemy type reskinned 100 times, enemies that are easily stun-locked etc.
It is really not a outright bad game (just like HL2) but it should not be recommended to anybody that hasn't gotten the best of FPS out of the way first. This would even, reluctantly, include Half-Life 1.
Doom, Half-Life 1, Build Engine Trio (Duke Nukem 3D/Blood/Shadow Warrior), Some kind of 6dof game at least one is essential playing (Descent/Overload or the goated Everspace). Maybe Quake or Unreal. At least one REAL console shooter like Turok, Doom 64 or Brahma Force. Ashes Afterglow for a modern take on 90s glory. None of these are 2000s-era games. There are modern games in this list, but not 2000s era shite. After that, then you should be upgraded to monocled. Without that context, one's opinion is not worth much. Again, please don't shoot the messenger! I am here to shoot down decline and spread the gospel of incline. It is for your benefit and the integrity of the industry.