(As I recall, the generic term for a non-IBM PC tended to be "microcomputer" or "micro" rather than "PC".)
That trend then leapt forward when Compaq started making PC clones. The clonemakers needed a word for what they were making. There was a time when you could call them "IBM compatibles", "PC compatibles", or "PC clones", but once IBM switched to PS/2 and OS/2 -- and proceeded to fade from dominance -- continuing to associate the word IBM with these things made little sense. Meanwhile, Apple wasn't trying to contest the term PC... instead they invented their own exclusive brand name, Macintosh, and sold the hell out of that.
So in the end the word PC ended up meaning a generic Intel box that runs Microsoft Windows or Linux.
Compaq won the white-room reverse engineering suits against IBM, opening the door for dozens of manufacturers to make clones of the IBM PC/XT/AT.
Eventually the term "PC Clone" got shortened to "PC" when referring to anything that was compatible with the PC-AT standard.