The design of this game harkens back to the days of the 2D football titles in the mold of Tecmo Bowl, when graphics weren't all that important. What mattered was play calling and execution. There was no such thing as a "juke stick" or a "Playmaker button." The fun part of those games came down to strategy, and maybe a little bit of luck.
Atari Football tries to recapture that style, presenting a horizontal gridiron with helmets instead of player models. But it uses a radically downsized playbook that's cut down to just eight plays each for offense and defense. It's pass and run, performed with simple finger gestures in the desired direction. There's no special teams, so it's four downs and out.