"In 1982 a cascade of computers beeped and blipped their way into the American office, the American school, the American home. The 'information revolution' that futurists have long predicted has arrived.... The creamy white [IBM] PC (for personal computer), introduced in August 1981, has set a standard of excellence for the industry." Time, January 3, 1983
And so the word PC, which originally designated a particular IBM model, became the general term for the whole category of personal computers.
Since then, of course, IBM has stopped making PCs, and PC's meaning has become less encompassing: it now generally refers to a machine running Windows.
(Meanwhile, PC meaning "politically correct" would have to wait for another decade.)