I feel Smash characters should be built more on the character than the game - let's say you have a fast paced one-hit-death puzzle game, but the protag is a meaty meathead, I would make the moveset based more on digetic details with a few references to gameplay here and there. A trapper moveset would feel more like playing their game, but a heavy-hitter or grappler would feel like actually playing as the character.
There are exceptions to this, Steve for example is a brilliant fighter because of his elements taken from the source material, but for the most part if you want people to feel like they're playing another game within Smash it'd be best done through gimmicky stages. Wario is a good example, Wario in Smash doesn't really feel like playing a Wario Land or Ware game, but you can get a good feel for the idea of Wario as character: a strong but uneasy guy with more cunning than he lets on - and if you want to play WarioWare within Smash, there's a stage for that.