Description taken from Game Boy version of this game

There is no escaping everyone's favorite plumber. In Alleyway, you tell Mario which way to go as he pilots a paddle to break every block on a given screen with a devastating bouncing ball. That's it!

A block-destroying ball bounces around a screen, and it's Mario's responsibility to command a paddle like a flipper in a pinball game, without allowing the ball to get behind him. The plumber must angle the ball so it takes out as many blocks as possible, formations that can be everything from simple rectangular masses to moving compounds. Adding to the challenge, the ball moves faster in some levels as Mario's paddle gets smaller. In bonus stages, the blocks take the shape of popular Nintendo characters. There are 32 stages to test Mario 's paddle-piloting abilities, but don't get him hooked on it, plumbing pays better. ~ Christopher Michael Baker, All Game Guide