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I would say the other way around, disputing what I wrote shows a fundamental lack of understanding the time period in which these personal computers came: it was a personal computer at home which the average person could finally afford. A computer that did not cost one million dollars but could run the same types of computations. In that sense, home computers of the day were personal computers, and they were designed to be generic enough to also be able to generate audio, perform desktop publishing and play games as well. The big machines like the General Electric and the PDP-1 and later on PDP-9 and PDP-11 were the breeding ground for the nascent game industry, since the very first games were programmed on them, so in that sense, playing on one's home computer doesn't make it any less of a personal computer. Personal computing is a usage paradigm, and we sure used our home computers for personal computing. And usually only one person used the machine back in the day.

Multiple people using the same system didn't come around until the advent of the average Joe going onto the InterNet.