Video games and weirdness are no strangers to each other. You could argue that Breakout is a decidedly weird game because it's like bouncing a ball off a brick wall, but each time the ball hit a brick, the brick disappears! Some have argued that Breakout was the first true video game as the game could not exist outside the video game format.
But, if we can take some strangeness and outright abstraction as normal, there are still a few games that leave me scratching my head.
Swinging Singles is one of those adult games, but being from the early 80's, it's very crude. It kind of makes me wonder why they bothered since it was from before digitized porn. There's a game called Streaking that's also from that era that features a nude woman in a Pac-Man clone. The weirdest thing about that one is not that the carpet matches the drapes but that there's a fatigue meter. When eating dots, the meter stay low, but running around without eating dots will cause the meter to go up and you'll lose a life. Why that was considered a good idea, I'll never know.
Amidar always puzzled me for some reason. It contains alternating levels. on the fist level, you're a gorilla who must dodge headhunter-type natives while gathering coconuts. So far, it makes sense. But on the second level, you're a paint roller who must dodge pigs. I don't know why I spend s much time wondering what the hell pigs have against paint rollers, but that's not the weirdest feature. The weirdest feature is that you have a jump button, but when you press it, you don't jump. The enemies do and you duck under them. No, really. You do have a limited number of jumps, so that may be why.
In a similar vein, Dancing Eyes features a similar maze gameplay to Amidar, but the maze is on a 3D modeled girl and clearing areas of the maze makes her clothes disappear. I mean, good lord!
Getting away from porn games, Sol Divide is a weird side-scrolling shooter because your character is a fantasy character and you have a melee attack. I mean, how many shmups have a melee attack?
Snacks'n Jackson features a guy in old-style hobo clown make up bouncing his nose off his face like a paddle ball game while stretching his neck out to eat floating food. Somehow, it makes more sense when you just describe it.
Join'Em puts you in control of like five little creatures in a maze. they are all controlled by one joystick. the idea is to use the maze walls to bring them all together and make one big guy while also dodging enemies.
Libble Rabble was from the creator of Pac-Man and used two joystick to move two pointers to surround various areas of the screen to trap enemies and reveal secrets. it was not as popular as Pac-man.
Those are just some of the weirder ones off the top of my head.