Huh, I'm pretty sure this was just an intro cut-scenes and that's it. Even Sakurai said to let our imagination fill the rest. I honestly don't expect much than the intro and an ending cutscene.
Especially with Sakurai saying that the mode will be more about 'fun than story'. I think we will get the big intro and ending cut-scenes, and some minor ones sprinkled throughout, like the scene from the Direct where the Inkling girl walks into the lair of the armored rhino dude, but not to the level that we saw in subspace emissary where a story moment happens between every fight.