Every school teacher of the day had a drawer full of those things. It was one of those "You'll get this back at the end of the year" items that they used to confiscate from the guys when they would play with them in class.

That's what I thought it was. I loved that game! I played my brother's all the time.

It was Mattel Football (white case) and was the "have to have item" of Christmas 1977.
By today's standards it was extremely primitive. It consisted of a series of LEDs, one bright one that represented the player and several dimmer ones that represented the opposing team. The object was to run the ball into the end zone with out colliding (getting tackled) by the opposing team members. The player could move up, down and in one lateral direction towards the goal. It actually took several trips across the screen to reach the goal.
A later version, Mattel Football II (green case), added passing and the ability to run in four directions.
And, yes, it was very obnoxious with all kinds of beeps and low-tech sound effects that could not be turned off (later "nostalgia" versions added a sound off switch).

My sister had a game like that but was a baseball game.

WAY back then there was an old electronic football game that had tiny led lights in it. You could pass and run. Tecmo Football, I think it was.