Just out of curiosity, have you also configured in-game settings to your likings for each one of them? Such as their respective resolutions, other settings, difficulty levels (when available of course) and so on? Or are most of them simply installed? Additionally, are all of them also patched to their respective last version? And, finally, do you count DLCs, Steam games or other digitally purchased games and Free-to-Play ones if you have any?
Anyway, it's impressive. I got about a total of maybe half of those games (I think around 420 or so, I'd have to check again) and they're all scattered across multiple older consoles, along with the PC. And I have yet to actually complete a good 70% of them. Ironically enough (well I think it's ironic in a sense) I happen to complete more games since the past few years than I used to back in the 8-Bit, 16-Bit and 32-Bit days, but one of the reason for that is because back then until I got my original PS1 I used to rent games instead and rarely had the time or the money to rent them again and again to eventually complete them, unless of course they happened to be short and could be finished in about a day or two (which did happen, but not often).
I have to ask, really, can you tell by heart (or your estimation) how many of those installed games you've actually played and completed yourself?