Yes, that is the original definition. But the common substitution of simply saying "PC" instead of "PC running a Microsoft OS" began when IBM named their first PC (in the original sense) the "IBM PC". IBM PC compatible machines were called "PC clones", and later also simply "PCs". Subsequently, any machine running a Microsoft OS from DOS through all the various versions of Windows has been identified as a "PC".
It's somewhat analogous to why we often call the U.S.A. "America". Because although there are many other nations in North, Central and South America; none of them has the actual word "America" in their names.