The platform list is telling me that Super Mario Bros. can be played on an SNES Classic edition. I own one of these consoles but I cannot find Super Mario Bros. After googling the closest I could get was finding a hack to add games, but the list for SNES Classic games on speedrun.com doesn't have these games. This must mean that Super Mario Bros. can be played on SNES Classic edition without hacks. Can someone tell me how to do this?

from what I understand that is included due to the inclusion of the All-Stars categories (under misc), which is a game for the SNES

But on the SNES Classic Edition, I can't find all-stars. Do you know how to access Mario All-stars on the SNES Classic?

You have to hack it and add more SNES roms. It IS legal on this leaderboard, there are already verified runs with it.