Er, not to me sarcastic, but Left 4 Dead 2 is made by Valve, and Valve ARE Steam, there is no non-steam version of Left 4 Dead 2 unless it's an illegal copy. ALL left 4 Dead 2 copies are steam, so there will be no non-steam version of the trainer.
Also, I followed the trainer instructions, press F1 when you are in FIRST PERSON MODE as in DURING A LEVEL where your shooting, not at the main menu like most CH trainers, after deleting the .dat file in the directory where your L4D2 trainer is and it auto-updates correctly, then restart L4D2 and the trainer and it works perfectly fine.
Instructions are awesome and work fine for me! if yours aren't then it's likely something blocking the trainer from updating, AV's / Firewalls etc