Oh I really hate Disney characters, but it was a really good idea of Nintendo in the eighties to license several Game & Watch games from them.
Mickey Mouse is basically the same as Egg, except the wolf has been changed for that lame Mickey Mouse who collects eggs for his stupid girlfriend.
Thanks to the Disney license, the game is cuter than Egg. Instead of playing a nasty wolf that steals eggs, you now play Mickey that collects them for his girl.
Perhaps Nintendo got the idea that some of the Game & Watch games were too aggressive or negative and then re-released Egg as Mickey Mouse.
Have a look at Fire Attack, Egg, Vermin or Judge to see what I mean by agressive or negative games.