LordHypnos opened an interesting thread
about games with good score systems that are not shmups (thanks, LH). Out of curiosity, I checked how many games involve mechanics similar to
Pirate Ship Higemaru, mentioned in the thread. The game is simple: a pirate must push rolling barrels against enemy pirates, and squash as many enemies as possible on each single screen. These games qualify as clones/variants of
Pengo clones, as the first title by Coreland/Sega appeared in 1982 and introduced the concept. A long list is on
Moby Games, the game database financially backed by Atari, and also includes Capcom's
Don't Pull, from
Three Wonders.
A variant originates in Technos'
Dommy (1983), in which a funny-looking character pushes various objects and squashes enemies who end up being under these falling object (e.g. push one wall in the left direction, the tile falls in the next space to the left and hopefully squashes an enemy).
Mr. Jong (Kiwako, 1983), with Mahjong tiles squashing enemies. Namco's ultra-cute
Rompers is a 1989 interpretation in which a young farmer must rescue his betrothed from a demon princess. He must thus squash ultra-cutesy enemies across 64 (!) stages. It is a Namco game, i.e. progressively difficult until it becomes a nightmarish challenge.
Don't we all love ultra-cutesy violence condensed in one single screen of love?

"The only desire the Culture could not satisfy from within itself was one common to both the descendants of its original human stock and the machines [...]: the urge not to feel useless."
I.M. Banks, "Consider Phlebas" (1988: 43).