I think the key characteristics of the Umihara Kawase games are 1/ deep physics-based gameplay producing a high learning curve, 2/ short, well-polished levels on a timer, and 3/ expect the player to attempt many runs. The following tick all three pretty closely (listed in no particular order):
N+. Nice platforming physics, really polished game.
Elastomania. It looks like an MS Paint nightmare but the gameplay is just fantastic. Early forerunner of the Trials games - play those instead if the graphics are a deal-breaker.
The first four main Tony Hawks Pro Skater games. I got really deep into 2.
Honorary mentions:
Pinball. Seek out a real-life table, ideally, but Pinball FX 3 (on a rotated monitor if possible) is still a pretty good time.
Particle Mace, kind of like Asteroids but you're swinging a mace around your ship instead of shooting - fantastically entertaining physics engine, but the levels are variations on modifiers, more or less.
Geometry Wars, iterative twin-stick arena shooter with a ridiculous skill ceiling. Skip the sequels, they just dilute the greatness.
Tetris, ticks 2/ and 3/ depending on mode but debatably lacks the deep physics. Definitely gives me the same kind of endorphin rush that the UK games do, and after thousands of hours over 20+ years I'm still noticeably improving.
Roguelikes in general, like Spelunky, Downwell and Isaac - may not have complex physics but they prioritise quick thinking and many runs at the same game.
Finally, I left out Remnants of Naezith because it's a bit too close to being a clone and because I didn't really get into it, but I'd describe it as "Umihara Kawase meets N+", so it feels like it should definitely get a mention.
