Understanding the story from the cutscenes only is funny, I have no idea what goes on. Without looking over this is what I think the story is...
First of all, nintendo characters like to have friendly fights. When someone beats someone up they turn into a trophy, so after someone wins they bring them back to life...
Now for the main part
in a lake(or somewhere) 2 robs go and blow up stuff with a bomb(Oh noez!)The bombs were created at the subspace bomb factory and they are leaded by Ancient Minister(another ROB really though). for some odd reason the aincient minister feels guilty. diddy kong and donkey kong come out of nowhere and have nothing to do with the plot. Wario goes around stealing trophies, but kind dedede steals the stolen trophies. link beats up a fake peach and mario misunderstands and gets pissed(lol, I couldn't help but laugh there). Then they go to the bomb factory. Ganondorf tells the robs what to do. 50 billion bombs are going to explode now, mario and those people barely get away and the awesome music starts playing(Its so catchy I learned it on keyboard and make a piano version
). THEN, the ancient ministers costume comes off and its really a ROB. Ganondorf also was giving bowser instructions earlier to do some stuff... Then Someone makes all your people trophies. You go to subspace to get them back. You then have to go to the great maze(Oh noez again!) For some reason this guy named tabuu is the leader and sonic horribly enters the game...you winand the bombs just somehow like go back in time or something(lulzwtf)
Yes I was trying to sound like a noob, But thats really what I got about the story
Most of it from the titles of the cutscenes, they helped a LOT, lol.