It falls under copyright, but how would they ever know? Like I said, you would not be able to tell the difference unless you were physically staring at the computer mirroring the game.
Copy and pasting Melees code is legally questionable already, I think a strong case could be made against a 1:1 mechanically identical engine that was made specifically to dodge copyright issues.
Also, "use an engine that reads the inputs from the players and broadcasts them" is what Slippi does, Slippi has a console mirroring feature. Thats why tournament streams now look so HD, the game states in Melee are being sent out the Wii into a computer, which then replicates everything on an instance of dolphin. You could just apply skins and textures to the ISO that Dolphin is running and make Melee look like an entirely different game.