Let’s say the PC doesn’t count and you aren’t taking into account backwards compatibility, emulation, online play, homebrew games, and the cost/availability of games.
I feel like I’d want to choose the PS3. Like the Xbox 360 it had a decent lifespan and a lot of games were produced for it. A lot of which are already some of my favorites.
The only things that would make hesitant are I feel like a lot of modern games are larger and have open worlds which I feel like that could be nice in the long run and many of my favorite games for the PS3 have been re-released.


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Yes, it can run all that. You may have to jump through a few hoops (just like in the case of the Steam Deck, just different hoops), but it can run all that.
I’ll also turn your question back to you: how many people use the Steam Deck for productivity, rather than for gaming, which is its intended purpose? And does it matter?
Like it or not, the steam deck is a gaming console, even if you can run non-game stuff on it too. Heck, even stuff like the Game Boy had (official!) accessories like the Game Boy Camera and Game Boy Printer, which were both useful outside of gaming. Does that stop the Game Boy from being a (retro) gaming console? There’s an ongoing project to provide productivity apps for the Game Boy (though, arguably, it did not ship yet, but you can extend the game boy with a cartridge in whatever way you can imagine).
Or, you can use your SNES as a MIDI Synthesizer (https://www.supermidipak.com/)! No modding or anything necessary, it’s just a regular cartridge. Can it be used for fun? Yes. Is it a game? No. You can do a lot of stuff with an SNES cartridge that has nothing to do with gaming. There was even a cartridge that let you play online games on the SNES (https://en.wikipedia.org/wiki/XBAND) - but not only games, it also let you read and write messages to other people. You didn’t need to go into “desktop mode”, nor install a browser, nor do anything special. You plugged in the cartridge, and it worked. It was far less locked down than the XBox or even the Steam Deck! Does that disqualify the SNES (or the game boy) from being a gaming console?
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So then a Game Boy is a PC, and so is the SNES, and the SEGA Genesis. Cool, cool, makes perfect sense.
Myself, I think the wikipedia definition is far better than yours.
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There’s a very important difference between what you can do with a thing, and what the thing was intended for, and what it is best at doing.
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