The way you're defining it, then this is clearly in the second category. The game definitely has characters. I'm just not sure why the distinction is worthwhile.
On a semi-related note, I think that a Wii Sports type game with a structure similar to this might be fun. Maybe get the golf story guys to work on it.
It's worthwhile because it gives games more of a Nintendo identity than a plain concept. If another game company ripped off Splatoon, the market at large would still recognize Splatoon as the defining original. On the other hand, if another game company ripped off Brain Training, Nintendo wouldn't have built-in recognition of their own work.
It's not entirely black and white though. Wii Sports doesn't have characters, but "Wii" in its title carries an automatic connotation with the Wii console which in turn is tied together with people thinking of Nintendo.
Ring Fit Adventure does have a few characters (Ringo, Drako, the four trainers), so it's closer to Splatoon than Brain Training, but none of those characters can be as iconic as the nameless inklings. That's why dealing with only two categories makes things tricky; a spectrum would make more sense.