"by definition" is a little harsh, and "with an x86 processor" is a little too narrow:
"The designation "PC", as used in much of personal computer history, has not meant "personal computer" generally, but rather an x86 computer capable of running the same software that a contemporary IBM PC could.":
"The designation "PC", as used in much of personal computer history, has not meant "personal computer" generally, but rather an x86 computer capable of running the same software that a contemporary IBM PC could.":
https://en.m.wikipedia.org/wiki/IBM_PC_compatible