Meaning of "PC" in "PC Engine"?

PC literally just means personal computer - a computer owned by a person rather than an organization like a corporation, university, or computing club. The term is roughly synonymous with microcomputer with an additional implication of a price point measured in thousands (or less) rather than tens of thousands of dollars. Contrasting terms are mainframe computer or minicomputer, describing systems physically too large for most individuals to own.

The contraction of IBM PC to just PC took place in the early 90s as the IBM PC (and more importantly, IBM-compatible PCs) came to dominate the personal computer market.

That market shift was not inevitable in 1987 when the PC Engine was released, and the domination didn't happen in Japan until even later (where you saw IBM PCs but also a lot of NEC PCs).

Based on these pictures, the PC Engine was meant to sit in the center of a case or housing for a personal computer.