Drew Breese might be very recognisable in North America, but American Football is not a global sport. Most people outside the US wouldn't have a clue who he is, never mind what he looks like and what he has done. I've watched a reasonable amount of American Football and Ice Hockey (can't watch Baseball, can't understand any attraction to it), but wouldn't recognise a single player in the store. I could recognise more NBA stars than NHL or NFL stars, despite having watched far less games. Running is more global, but is more niche when it comes to stardom. Usain Bolt is probably one of the most recognisable sportsman around the world (as were Flo-Jo and Carl Lewis in the 80's) - but distance runners less so (Mo Farah very recognisable here in the UK, but I don't know how famous outside these isles).
Proper football (association) is the global sport with many recognisable stars, and probably has the biggest stars (Cristiano Ronaldo and Lionel Messi would be recognised around most of the world). Tiger Woods is sports star who transcends his sport. There have been many boxers (heavyweight usually) who've been globally recognisable - Muhammed Ali, Mike Tyson.