This refers to the other meaning of "Personal Computer", this time with capitalised initials because by convention it means the IBM PC, a particular type of micro-computer introduced in 1980. It was not a new invention, just another design of micro. It was not even a particularly good design, but it sold (mainly to corporations at first), because the IBM name was on it. If it can be said to have been invented at all, IBM did so.

The heart of the original IBM PC, the central processing unit [CPU] chip, was the Intel 8088, which was a cheaper version of the 8086 and used the x86-16 instruction set. Intel's 8086 and 8088 chips existed before either IBM or Microsoft became involved with them. All present day PCs (by definition) use descendants of the 8086 and extended versions of the original instruction set.

What Gates did was to sell IBM an operating system for the original IBM PC. It was DOS, which Microsoft bought from elsewhere and re-packaged. It wasn't much good but it was all they had. Ever since, Microsoft have continued to sell operating systems for the descendants of the original PC.

No invention by Gates was involved.