I think obtuse or odd was the word you meant in the title, in any of the three cases my example is "Space Station Silicon Valley" for the Nintendo 64. In this game you play as a broken robot on a space station filled with artificial animals. And by that I mean things like robot dogs, foxes, mice, gorillas, lions, sharks, penguins, bears, snakes, sheep, and so on. Now the gameplay itself is such that you are not but a microchip, with legs apparently, that can take control of inactive animals and use their abilities.
Your goal is escape, and to do so you must collect pieces of your broken spaceship scattered about the station (I think, though I can never prove it, that this game was part of the inspiration for pikmin, they even both start with an asteroid smashing your ship). To get these pieces you must accomplish various objectives that open up new pathways through the station, and to do that you will have to use the various unique abilities of the fabricated fauna. Some will have basic attacks, others have long jumps or other utilities, and some shoot rockets. Of course to access a lot of the mechanical wildlife you must first render it unconcious, or inactive I suppose, which generally requires a good bit of combat.
I don't actually know how obscure the game is, but I'm certainly the only person I know whose played it.
