They weren't gaming first, they were gaming only. You didn't load up an office program on an atari or snes. That didn't really change until they combined them for media purposes, like playing CDs, DVDs & BDs, and even that was extremely limited and without consistency.
No idea what your homebrew / piracy paragraph is supposed to be in regards to this topic though. That's not just not official, but straight up "illegal" in the minds of their creators. As a kid I personally owned one of those SNES adapters where you'd plug in a floppy disk and would rip the game from the cardridge into a rom. If we were caught with that we might've even got into legal trouble. On a Deck you can copy & paste all the files you want. You can download and run all the programs you want, albeit a tiny bit more restricted than your regular desktop distro. But in essence, it's still a full fledged PC, with everything that comes with it, and you could use it just for non gaming purposes if you so wish.
It's simply that. A Linux PC in a handheld format.