Oldest game I own, full stop is crystalis. I have owned it since I bought it new in 1990, but right now it's at my parents house. My oldest game "on hand" is probably Final fantasy Adventure (for Game boy) bought in early 90s but not likely new.
Oldest console game on hand is star Ocean 2 (PSX). Got it in a grab bag when I bought my PS1 second hand in 2000.
Oldest game that I know I am the single owner of that I have on hand? That's a much tougher question because I bought a ton of game it games used and all my consoles before the PlayStation are not "on hand"..
Revelations the demon slayer I got new in 1999, Probably that one (if I didn't buy FFA new).
TL
R. Final fantasy adventure or crystalis (depending if you count on hand or in storage)