I have made a preliminary fix for the issue you added but I don't have this game and it doesn't seem to happen with the demos; could you try it?
Topic on User talk:ThatOneReaper
Hitman: Codename 47 frame rate fix test
So I finally got around to looking at this patch. Sorry it took so long.
Anyways, when I booted up the game, there were no frame rate issues I experienced. The entire thing ran at a constant 60 FPS.
Someone in the commit history mentioned that the issue may have been Windows 8/8.1-specific, but I can't confirm that.