If you're talking about the 1984 MUSE game, I just gave it a spin on my XT. It's not exactly as you describe, but when I start a new game, it draws the starting room (slowly enough), immediately goes "You're caught !" and that's it. Then it gets itself into a loop ("Loading demo", "You're caught !", "Loading demo", "You're caught !", rinse and repeat) and needs a Vulcan nerve-pinch to snap out of it.
So it's not that it runs too fast - it doesn't get a chance to run much at all before it craps the bed. My copy isn't original either, so this could be one of those poor deprotection attempts that were only tested on emulators or >386 systems.
EDIT: a little bird tells me "this game requires DOS 2.1 or earlier". I don't really feel like writing more boot floppies at the moment, but that's one thing to try, I guess.