The whole game is definitely there, and if it isn't they hid it very carefully. In Zelda 1, I killed myself, went back to the title screen, named myself ZELDA, and made it as far as the third room of the first dungeon of the second quest! Do you really think they would have second quest stuff in Zelda 1 if it weren't the full game? Also, if you're curious, the name of the file you start on in Zelda 1 is "LINK". The fact that I was able to load Luigi as a character in both Super Mario Brothers and Super Mario Brothers 2 should also be a hint. In Donkey Kong, I was able to make it back to the title screen (the demo ended before I could start a new game, but it's definitely the NES version of Donkey Kong so no 50m) and able to make it to 100m. Editing games this carefully to make sure literally everything you can do in the time limit is there but nothing else would require a lot of work; just including the full game is the logical thing. It obviously runs on the Wii's internal emulators as well, given that it would accept input from the second controller for Luigi in Super Mario Bros.
What pretty much all the games did was copy the full game, add a timer, and have the game automatically load a "save state" when you boot it up. The fact that the OoT adult Link file starts off injured suggests this more than anything. The only case in which this does not seem to be true is the "ready to enter the Deku Tree" file in Ocarina of Time which seems like a hacked file, but just because they cheated in making a save doesn't mean the game is otherwise not there.
