I guess in recent generations, when we have the graphical effects, and high enough resolution to present detail, you can go for stylistic approaches like that, and it's really obvious. Take Yoshi's Story, Paper Mario, and Kirby's Epic Yarn as examples. If a game was meant to look like a stage play, it would be so much more clear that it was so. Back in the NES days, when you don't have a lot of colour options or the resolution, and probably sprite size restrictions, and everyone's just trying to make graphics of something that even look like what they're supposed to represent, it's actually really neat that they made a choice like that to make it appear like a play, and yet still kind of funny that most of us hadn't thought of it that way. I wonder if the new Super Mario game for the 3DS, that looks like a spiritual successor to Super Mario Bros. 3, will be that way. But given the 3D nature...probably not.
(Remember Clay Fighter (and its sequels, and Claymates)? It seemed cool at the time, but looking back...not really. The Super NES has more colours than the NES, but the same resolution, so the "clay" appearance doesn't look as great as I remember. Regardless, I do like that they at least attempted to do something different, not all this hyper-realistic stuff that seems to be the norm these days.)
The EarthBound stuff is freaky, but that fleshy Giygas cave I always figured was like some biomechanical
H. R. Giger horror stuff (like the Alien movies and the Dark Seed games). (Giygas and Giger...hmmm.) Still a bizarre final boss for a game that started out cute and colourful. I played but don't remember much of Mother/EarthBound Zero, but from what I do remember about Mother 3, there always seems to be darkness underneath the colourful appearance of these games. A death fairly early in Mother 3 surprised and even shocked me, and I remember thinking that the swatting death of Buzz Buzz (or whatever his name is, you know, the bee guy) early in EarthBound seemed like really twisted humour.