There are a few exceptions or probable exceptions to the "originate in a video game" rule. One seems to be if you're a Nintendo product in general. Though tbf, things like ROB and Super Scope are still peripherals; gaming products even if not software or hardware.
Another is you can debut in another medium if that material's purpose is to tie into a game, even if the game arrives later. Like Lucario, Togepi, or, probably, Strider.
The last is if a gaming universe has a specific incarnation of a public domain character or a real life person. Like Castlevania's Dracula, Kid Icarus' Medusa, and, probably Codename STEAM's Lincoln.
Those seem acceptable. The grey area begins with characters who debuted in video games, but in a series that didn't begin as a gaming one, like Android 21, Starkiller, Aya Brea, or V, from Cyberpunk. I suspect that they would avoid series that are not known primarily as gaming series, like the former two, while the latter two are likelier from a theoretical perspective, as most people, to my knowledge, associate Parasite Eve and Cyberpunk with the game(s).
And that raises the question of someone like Geralt, who did not debut in a game. I know the Witcher games are bigger than the books, and I know they take liberties... but at the end of the day, Geralt is a character who debuted in literature, not gaming, and Witcher began as a literary series, not gaming. He's also a grey area, but I would lean closer towards him being ineligible.
That also throws a character like Hatsune Miku into consideration, who debuted in not a game, but what is still digital software. I'd say she's the biggest grey area. It could go either way, but if you're being strictly literal, Vocaloid isn't a game, and she wouldn't qualify.
Things like Tamagotchi are games though, albeit very rudimentary ones, so they and Digimon would qualify.
That's where I stand on all these more complicated cases.