I enjoyed some of the old DOS games...but I believe by "home computer" was meant a console that was not meant to be a general-purpose PC while still allowing people to create programs on it rather than relying on pre-manufactured games for all entertainment.
The Commodore 64, ZX Spectrum, and Sega SC-3000/SF-7000 (the branch-off from the SG-1000 that did
not become the Master System) were home computers; they were primarily intended for gaming but it was possible to program also, commonly in a dialect of BASIC.
This article summarizes them well:
http://en.wikipedia.org/wiki/Home_computer
BTW my household was primarily a "Nintendo household" (as opposed to "Sega" and later "Sony") although we did end up getting a Genesis, Sega CD, 32X, and GameGear in 1994 shortly before the Saturn came out (and never got a Saturn).