> If "x64" can refer to amd64 or Intel 64, then it can also refer to PPC64, aarch64, mips64, et cetera.
No, it cannot. It refers exactly to AMD64 (not "amd64", it's a GCC's marketing name) and Intel 64 (and their previous revisions) and nothing else. See, I too can omit middle terms in a logical sequence and simply assert the conclusion (You've omitted something like "and if the name can denote two things it may as well denote any number of things with vaguely similar alternative names" which is obviously ridiculous).
> "Intel 64" could refer to Itanic
By your own logic it could not. "Itanium" is a marketing name, the architecture's actual name was "IA-64".
The things have names that people put on them. If people refer to AMD64 as "x64", then "x64" is a name of that thing, literally. Whether it's correct or not is a matter of convention and popularity, and your proposed convention is quite unpopular, I'd say.