What does the OED say a "mechanic" is? I'll wager it's different from "mechanics."
My OAD says that a mechanic is a skilled workman, while mechanics is (yes, it's singular) the scientific study of motion and force. Since I'd say RPGs don't quite fit that bill, I can go down the line a bit further and start to answer
@Yora 's question with these not-quite-matching definitions:
Mechanics: the processes by which something is done.
Mechanism: the process by which something is done.
So no, a rule isn't a game mechanic. You can't take a singular word (mechanics) and pry the s off to make it more singular. At least, not in English. Jd (see above) is close: rules can describe a process, which can in turn join other processes so something can be done (mechanics). But it's probably more correct to say "rules constitute mechanics" than "rules = mechanics."