to the best of my understanding—but please correct me if I'm mistaken—Miyamoto is not, and never really has been, what we would traditionally call a "game designer"—from what I can tell from reading numerous interviews, both with him and others who worked with him over the years, he's more like a Steve Jobs-type figure. he comes up with a broad interesting idea or set of ideas or even just general vibe, and then it's up to the programmers (and probably game designers nowadays) to figure out how to turn those ideas into an actual game. then he sees what they've come up with and gives feedback; rinse and repeat until the game ships.

with regards to paper prototyping though, while I believe it can be a useful tool in certain situations, I pretty strongly believe that its usefulness is being vastly oversold to aspiring video game designers, these days. the best use for paper prototyping is when the game you're setting out to make strongly resembles an analog game—like a roguelite deckbuilder, or Fortune Street. but if you're looking to create a design for a video game that truly embraces what's unique about the medium—instead of just making a computer-adjudicated board game—then there really isn't a better way to do it than just biting the bullet and prototyping the gameplay with code. in my opinion, the best-designed video games are not ones where the design was thought through to completion ahead of time before implementation began, but rather, ones where someone had an idea or two and sat down and started programming its implementation—prototype or otherwise—and the eventual design of the end product was discovered through playing around with the combinatoric outcomes of interesting rules and mechanics that interact in nontrivial and often unforeseeable ways, seeing what works and what doesn't, seeing what's interesting and what isn't, and gradually arriving at something special and unique.

many people disagree with my assessment here, because they want to believe that it's possible to create a design for a video game that is unique and interesting and special, whole-cloth, without ever writing a single line of code. but how can that even be possible? the main things that separate video game design from analog game design are 1.) the computer adjudicating the rules, and 2.) the much faster feedback loop between action taken action and observed outcome, from the perspective of the player. these are qualities inherent to the medium. you can choose to ignore them and design a more or less perfectly paper-prototypable game... but, if that's the case, perhaps you'd be better off designing a board game instead. just like how many AAA linear-narrative-focused games' narratives really would just work a lot better as a movie or TV series. now this isn't always strictly true of course—roguelite deckbuilders are fun as hell, even though they're generally very straightforward to paper-prototype. but again, of course these kinds of games lend themselves to paper prototyping, because they're really just essentially digital board games. and if that's all you ever want to make, then sure, go on ahead.

but if you want to make something that embraces the qualities of the medium that make it stand apart from its contemporaries, then really, making a digital prototype is the only way to go. as a hackneyed example, consider Braid: its initial prototype had a functioning "infinite rewind" system, and its designer/programmer implemented more or less every idea he had (including World 1, the final level)... but much of the rest of the mechanics (such as World 4's "current point in time for all other entities in the level = the player character's x-position") only came about—were arguably discovered—through the act of implementation, as opposed being done in advance of implementation. if whether or not Braid was made hinged upon the perceived success or failure of preliminary paper prototyping, then it's quite likely it would never have been made.

moreover, it is entirely possible to design a game through paper prototyping, and be reasonably satisfied with the design... only for you to then implement it and actually play it in the form of an actual video game, and find it to be underwhelming, unengaging, or otherwise completely unlike how you envisioned it with your abstracted paper prototype. for example, that page of 300 video game design ideas are likely mostly or entirely interesting at face value—but without being tested, are basically entirely meaningless. I just clicked on a random one: https://www.squidi.net/three/entry.php?id=224 this is a cute idea, but without even testing it out myself at all I doubt it's actually very good at all. but hey, maybe I'm wrong, maybe it's the next Angry Birds, or something! I'm not faulting the author for posting it on their personal website, but really, it's nothing more than just a wholly untested, spontaneous idea jotted down in a notebook. until said idea is put into practice in the form of a playable video game prototype, there's no way of knowing whether it would actually be fun at all, or worthwhile to pursue developing further.

but, to my point above: perhaps in building and testing a prototypical two-button FPS game, the designer might realize that their idea was utter garbage... except for some small aspect that they did not and could not foresee. perhaps it's entirely incidental to the "two-button FPS" game idea. maybe it's even just something as trivial as a bugged shader that produces undesired yet unexpectedly visually interesting output, or improperly-implemented movement mechanics that inspire a completely different, first-person-shooting-less idea for a game.

conversely: if Vampire Survivors never existed, and you came to me with an idea for a single-stick no-button roguelite top-down shooter with barely-animated 2D sprites that look like they should be in a side-scroller instead, I would've thought your idea was mediocre at best, and not worth pursuing. but as it turns out, it's a great idea for a game, one that ended up spawning a whole subgenre—and anyone can see the appeal for themselves, just by playing it for only a few short minutes!

paper prototypes can be useful for designing certain parts of certain types of games, but I completely and vehemently disagree that they're a useful tool for determining whether or not a broad, abstract video game design idea is worth pursuing further.