There's no Mario (American) football game because...Mario himself has the power to kick a football into outer space.
Think about it; from a standstill, in SMB3, Mario could kick a presumably solid block of ice hard enough to get it moving at 3 pixels per frame. Assuming Mario's about 5'8" and 28 pixels tall (roughly), that makes a 16-pixel block about 1 meter on a side. Since ice has a density of roughly 917 kg/m
3, that means the ice block would weigh about 917 kg, and converting units makes 3px/frame = about 11.25 m/s. If Mario were to kick a football, which weighs about
430 grams tops, with the same force, it would end up going about 24,000 m/s (~Mach 70), or twice
Earth's escape velocity. Then again, gravity in Mario's world can be calculated to be about 10 times Earth's, but either way, that's a heck of a powerful kick.