Based on the videos on the landing page, I was getting the impression this was a VR/fitness game. Everybody running around had me thinking you needed to run in order to your avatar to do the same. I was actually disappointed how little you actually have to do to play the game when I navigated a couple screens in to get the full-picture.
The Mario Run big promo video[1] seems to have just copied the marketing approach for Pokemon Go[2]: feel epic and show people in real life. However, Pokemon Go actually involves walking around in the real world, but Super Mario Run does not at all.
Seems like a definite miss in the marketing message, since I thought the same as you on first watch. I even saw the announcement at the Apple Event, but upon seeing the first video ad Nintendo created, I thought, "wait, does this have a fitness element to it?"
Definitely makes me wonder what kind of fitness-minded games could be done by Nintendo, though!
