There is a C ABI. The "x86-64 System V ABI" (the ABI for C on everything except Windows on an x86-64, ie a typical PC) was designed by AMD working with early adopters on Linux and other platforms. Here are several extant ABI documents:
The ABI for C needs to agree less stuff than a C++ ABI but it's still quite a lot of stuff, if these things don't get agreed then code won't work unless everybody uses the same (version of the) compiler.
- Chrome OS (where JavaScript and WASM is what matters)
So no, it isn't everything except Windows on x86-64 and then there are all the other OSes running on ARM, MIPS, PowerPC, SPARC, PIC and plenty of other less relevant CPUs .
There is no such thing as C ABI, it only happens to work on OS that are, surprise surprise, written in C.