Football IS strategy. Every play is scripted. Position is excruciatingly defined, even by the rules, and the playbook is nothing but strategy.
Baseball is a knowledge of statistical probabilities and playing accordingly. Is that strategic? Yes, but not to the degree demanded by football.
Hockey, soccer and basketball rely much more on improvisation. Coaches install systems of play and demand that the players execute the system. Then they rely on the skill of the players to improvise within the system.
The way I see it, football is by far the most stratigic game. There is even strategy in the coin flip. The “game plan” is the script of the strategy an it continues right through to clock management.