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Why is this listed as a puzzle game? It's a "twitch action" game.
Good call — looking at Video Game Genres, I think Arcade Game is the best fit. I'd be willing to pull it from the Puzzle Game page and move it over if there's general agreement on that point.
The Arcade Game index is for games that have been released in arcades only.
What does "twitch action" mean, exactly? Given a definition, we could just create an index page for those games — searching for "twitch" on the site turns up some other games that might fit: Sinistar's page lists that game, Tempest, Defender, and Robotron2084 as "twitch games", and from what I've seen of Tempest and Defender I don't find that wholly implausible.
It's an Endless Running Game, except with polar coordinates. Or, picture a typical ERG with wrap-around.
Regarding A Winner Is You: that description doesn't sound like it really fits. It might not be an epic montage of epic epicness, but it's not just a bare "You Won" sticker on a static background.
I was kind of debating it myself, honestly, and I added it.
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How well does it match the trope?