It was expected that Nintendo would detail Super Smash Bro Ultimate’s story mode (assuming that there was one) in the 27 minute long Nintendo Direct, but they didn’t talk about there being a single player focused mode outside of the revamped Classic mode.
They did however, show a secret new mode, which they weren’t ready to reveal yet. As you can see in the image, it’s equally as important (based on size) as the main ‘Smash’ mode, but Nintendo weren’t ready to reveal it yet, suggesting that it’s something new.
Our money would be on a story or a boss rush mode, based on a few things.
Nintendo spoke about bosses a few times in the Nintendo Direct, but never indicated that they’d be bosses in Classic mode (or any mode for that fact), suggesting that they’d be apart of a separate mode.
Both Dracula from Castlevania as well as Rathalos from Monster Hunter were mentioned as bosses and shown off in depth. These could easily be mistaken as stage hazards, but in both instances where Nintendo showed them, it was only the boss as well as a single character on screen. If they were stage hazards, then Nintendo would have surely shown them off in a typical battle scenario.
It’s also been pointed out that neither of these stages could be seen in the overview that showed all the 103 stages that Nintendo showed off, indicating that these wouldn’t be typical stages.
The other point is the fact that Classic mode doesn’t appear under the ‘Smash’ menu, indicating that it probably comes under this other menu (which would assumedly be called Solo).
Lastly, and this one is a little bit looser. Someone has looked very closely at the pixelated menu and has determined it says ‘Spirits’ which could actually align with Luigi dying and clearly transcending into a spirit in the initial bit of the trailer.