I would assume football and hockey games are similar in that you could say you "beat" them when you finish a full season + win the Superbowl/Stanley Cup on Professional mode (stay with one player for their career, or whatever the equivalent in a football game would be).
I'm curious about this, since the best time I've seen for a tool-assisted speed run of Link's Awakening is 1hr05m., and that's using glitches to skip portions of the game.