Intellivision baseball- where the players looked like little mushrooms
Atari football where it was 3-on-3 and the players looked like something from monsters inc. We had a rule that you couldn't go "through" the tv screen as when a defensive player was at the edge of the screen they could pop out on the other side just by standing there making it easy to tackle a runner who had gotten ahead of the field. That rule and it's inability to be enforced led to many a live action punchout between me and my brother.

The football game I remember causing violence to ensue was an Atari arcade tabletop football game where one team was X's and the other team was O's. You had a bank of four plays to call from, and used a trac-ball to move to ballcarrier on offense and free safety on defense.
I figured out on defense you could call a play and your defense would set up to stop it. I failed to disclose this information to my usual opponent and went on a big winning streak. When this asymmetry of information was discovered, there were fisticuffs.