Interesting bit about the Sinclair, I learned BASIC programming on a Sinclair. I remember quite a few early cave shooters too, they've been around for a while. They tend to remind me of Sopwith, one of my favorite classics.
The cave shooter you first linked to could be easily done with variously shaped polygon Sprites. The second though, that'd require a bit of creative shaping of the Sprites, but fundamentally it'd be the same, just variously shaped, though textured, polygons.