Deadcore has a timer right on the gun you use in the game, Driver on GBC has a few categories that use an in game timer as well and is fine on emulator
I Just got Comic Jumper onto this site and has an in game timer for the stage, so it only counts for single lever runs, but its Xbox 360/one only
You may want to try Armed with Wings: Rearmed. It is not on the site yet but I already requested a series that will involve that game.
¤cough¤ All of the Monster Hunter games ¤cough¤ Metroid Prime Federation Force Fast Racing games Xenoblade Chronicles X (not rlly, but kinda)
The Disney Afternoon Collection got a time attack mode for some NES capcom games such as Ducktales / CnD / Darkwing duck etc. Not technically PC games, but rather NES ports, but might still apply.
Super Smash Bros. Melee has the all star modes of different difficulties as categories and they all keep time for you in game and there's no need for a split or any calculation.