to this run: https://www.speedrun.com/smw/run/m315wn6z

At 1:16:30 you see a Yoshi/"dragon" coin in Larrys Castle (Boss of World 7). I thought, only in the GBA-version of the game, castles had coins, too..?

So, is this really played on SNES?

Yes, this is played on SNES. The castles 5 and 7 are the only ones to have dragon coins in the SNES version.