We had a very old console, parents called it the family computer and it had cartridges. I remember playing a game when I was 7 wherein there were guys and they had bats and they would beat up people with it. There were 2 guys on the cartridge design I think, and they were buff like the Contra guys.

I only played it for a while but I remember being in an area and it was just a small one. Imagine a rectangle but without the borders. That was the limit I think. Enemies would then pop out from all sides and you had to beat them up.

EDIT: I guess I have to add more details to be more specific because this practically describes majority of the beat em up games.

I remember the background being dark, or just black. your buff dudes which you control had weapons similar to sticks and bats and I think they had biker jackets. The cover I was talking about looks very similar to the Double Dragon 3 cover. but the gameplay is vastly different, similar to Combattribes. My uncle and I never really got that far because we kept dying in the first level.