It really hasn't much to do with C (e.g. there is no such thing as a "C ABI", and especially no such thing as a "standardized C ABI" - not sure if that's even a hot-take anymore).
ABIs are defined by CPU and operating system vendors. Those ABIs usually happen to be quite 'C friendly', but that's not a requirement (for instance the AmigaOS ABI was primarily meant to be used from handwritten assembly code, and Amiga C compilers had to adapt to those ABI rules or they wouldn't be able to call into the operating system DLLs).
Yep, an ABI (function call convention) is computer language agnostic. It is a binary specification. And in real life, only a subset of it is actually used.
If they want to find something really obsolete, they better have a look at executable/dynamic lib file formats (PE+, ELF64). In other words, they better look at that first: I am using my own, which is beyond simple (a little RFC would suffice), no loader of any kind, basically userland syscalls. And I do embbed exes in an ELF64 capsule to run them transparently on linux systems (writting a internal linux exe loader would be copying ELF loading code while trashing 90% of its code). (hopefully in some not too far future, I'll try to build a mesa AMD vulkan driver for this very simple format and for that the main issue is.. c++ with its runtime, as always...).