so something that I find really interesting about Kai's powers in canon is that like. they don't actually impact his intelligence in any meaningful way. of course, there are a bunch of ways to measure intelligence, but the narrative shorthands for "this character is smart" don't really happen with him.
in fact, the others are a lot better at solving puzzles and analyzing situations than he is. I don't mean this as a slight against his character — I wouldn't be talking about the implications of his powers if I didn't frickin' love his character — but objectively, the others do seem to have better investigative and strategic skills (Mira's creative solutions like the waterspout, Adam's observational skills resulting in him figuring out they're in a game, Mira realizing before either of them that they weren't supposed to be there in season two, and so on).
what he does have is knowledge, and something that's way too easy to miss is that it isn't just technical knowledge. sure, he knows the carrying capacity of an electric cable just by looking at it, and he can apply that knowledge even on something as advanced as a spaceship, but he also knows things like, say, witches come in threes.
and like... that's the kind of thing that, even if he remembered it, wouldn't necessarily apply to the real world. and at the time, he thinks he's in the real world.
anyway, the point I'm making here is that I generally interpret his powers as having nothing to do with technology and everything to do with meta-level knowledge.
(on a meta level (ha), the intention of him being, iirc, the only character in the show to use the word 'meta' — "woah, that's meta. and kind of makes my head hurt" about Miles wanting to play video games with him — could be a subtle way to tie the character to the idea of video game self-referentiality. that would assume intentionality on the part of the writers, and honestly, I wouldn't be surprised)
it would make sense, then, why he has both realistic knowledge about things relating to the game mechanics ("there's some serious juice running through these cables") and technical knowledge that's... less realistic, ie fixing and flying a plane that has a standing takeoff mechanism (cannot imagine anyone actually designing one of those anytime in the next three centuries; if someone has or is trying to, the only question I have is why), and also being able to "stabilize the thrusters" by typing into a keyboard. The fire-powers propulsion thing would realistically give off way too much heat for him to do it anywhere near other people, which he would implicitly know if he was a scientific genius on all accounts... but which he wouldn't even consider if his knowledge is largely based off of video game mechanics, rather than real-world sciences.
and anyway, it wouldn't make sense for a video game to be able to imbue someone with technical expertise in a bunch of different scientific fields; it wouldn't make sense for the game developers to want to deal with that headache. not to mention, Kai makes a couple of small media references (Mermaid von Doolittle is, I presume, a reference to Dr. Doolittle), but the others don't really do the same. The one time I can think of that someone does, it's Adam recognizing the horsemen of the apocalypse, and I generally assume that concepts like that, which are pretty solidly entrenched in the culture and reiterated a thousand times in a thousand ways and what have you — that is, religious symbols in general — are probably not gonna get taken away by the memory block.
anyway. yes, I do incorporate this into his character in Project: HOLLOW, but since they're not in a video game, his knowledge isn't of a video game. instead, he understands some real-world mechanics and, rather than meta-level knowledge, he has the benefit of not getting totally fucked up every time he recovers a memory, and also of recovering clearer memories than the others. I digress.
