Are you telling me that when I browse the web,
Yes. WTF do you think web sites are hosted on?
play a game,
Stand-alone game, no. Multiplayer, almost certainly yes.
or run some other app on my phone/tablet
Depends on the app. If it is entirely self-contained - both on
the compute side and on the database/internet access no,
otherwise yes. E.g. fart app or jiggle boobs, ARM can handle
that no problem. Google maps, finding closest restaurant, or
updating facebook status etc certainly yes.
that it's running on an X86 server somewhere?
Don't get me wrong, the application processor is always
refreshing your pixels and looking for finger contact but
the useful stuff is almost always done at least in part if
not majority on a server somewhere. Without connectivity
to the cloud a smart phone is basically a Nintendo DS. :-D