Super Pinball by Electro-Plastics. Not common, it was a French company, there were several different versions of the game. Year is 1983.
You will probably NEVER find a board. Looks neat as it is though, I would keep it if I were you.
Similar games include Chicago Coin's Super Flipper, and I think there was one other, it is eluding me now, but the Electro-Plastics ones were the only ones in those teeny tiny shorty cabinets.
Or there is a mild chance that someone did a video conversion of a shorty type pinball, but I don't see any scoring stuff on the backglass.
Or this might also be a previously unknown game that just happened to be in a shorty pinball cabinet like the Electro-Plastic ones were. Yours is certainly different from the ones on their flyer, but has a few extreme similarities.