But you didn't comment about people not having beaten Doom. You said "have not played" it. :) I, for example, have played Doom (the shareware episode, anyway), but I haven't beaten it (probably not even that shareware version). And I know that the majority of people who buy or play any given game never play it to completion -- but that doesn't mean that they never played it. Hell, there are video games I've spent dozens, if not hundreds, of hours in that I've never finished. In many cases, I haven't even come close (though not always for lack of trying/lack of interest).
Any given person whose oldest mentioned game is post-'93 could've played Doom, but never finished it. Or they played and finished a friend's copy, or finished their or a parent's copy, but later sold or otherwise lost it (remember that owning the game is a qualification the OP made).

I mean, it's all good. I was just trying to point out the flaw in your reasoning. :)

The OP didn't provide any explication, and doesn't really come around here any more to ask.
What counts as "ownership" (and, indeed, having "beaten" the game) is kind of up to you. On the other hand, I definitely took "oldest" to mean going by absolute age (i.e, by date of initial release, or at least by release date of whatever particular port you may have played), not relative age (i.e., how long ago you bought or received your copy of the game, or completed it).

Almost forgot among making other replies, but thanks! I'll have to try that at some point. It seems things have progressed in the ease-of-use department since I last looked into how to run it on modern Windows a few years ago. :)

Probably Archon on the Commodore 64, first released in 1983. Although it's more of an MP game.

Oldest proper SP game (although it had co-op) was probably Katakis/Denaris (1988) also on the C64.