Every platform has an ABI, obviously, and yes it's generally formed in view of C.
This doesn't change the fact that the phrase "The C ABI" is, in a vacuum, meaningless and that "The C ABI on Platform X" is just a convoluted, cart-before-the-horse way of saying "Platform X's ABI"
Put another way, I'm arguing that "C" is a more useful descriptor than "platform X's", because the sentence "Rust is compatible with the C ABI" is short for "forall X, Rust on platform X is compatible with the C ABI on platform X", and means something different from "Rust is compatible with the SysV ABI" (which implies that it follows the SysV ABI on Windows and OS X, too). And since the typical way of doing that is by interfacing with a C compiler or the C library (... and you could make this exact argument about the phrase "C library", I think), it's worth mentioning C. For instance, Vala and Nim, which both compile to C, are always compatible with the C ABI. If you port them to a mainframe they remain compatible with the C ABI, but not with the native ABI.
It's sort of like saying that there's no such thing as "rules of the road", because the road makers don't specify how you're supposed to drive on them, and the rules differ by jurisdiction and sometimes you're in a wilderness with no roads. The term is commonly understood to mean "rules for using roads, in the road-containing jurisdiction which you're in". I think the same thing is true of the phrase "C ABI", although if people are coming away thinking there's a cross-platform C ABI, then yes, we should be more precise.