Naruto Shippuden: Ultimate Ninja Storm Revolution offers a couple of different story modes. One is called Ninja Escapades and is the aforementioned anime episodes while the others are contained in the World Tournament option.
Ninja Escapades lets you sit back and watch new stories unfold, but instead of keeping you out of the action, when it comes time for a fight, be ready to pick up your controller. After clearing the arena, the story continues until the next fight scene. Each episode seemed to go on rather long, even if you don't count the amount of time in the fights, so expect a lot of time to be spent here working your way through these new adventures.
The Ninja World Tournament Mode is a competition between many of the fighters in the Naruto world even "bending time and space" to grab characters that aren't contemporary with each other. While this mode takes on a standard tournament structure, there is time between matches where you explore the open world of Festival Island. Here you will talk to people, take on a few side quests, and buy tools to use in your fights.
The fights in the Ninja World Tournament are a little different than the standard fare. While you are still doing everything you can to knock your opponents out, they will shed orbs with every bit of damage they take. Your goal in these fights is not actually to take out your opponents, but to have collected the most orbs when the match ends.
You start this mode as a D-Ranked competitor. Each time you win the final fight in the tournament, you get the next rank and will fight a harder selection of enemies, but you will also get bigger rewards and unlock more characters. Completing the D-Ranked tournament also unlocks a separate story mode following the new character Mecha-Naruto.
The Mecha-Naruto story starts off when Naruto and Hinata find a robot that looks a lot like Naruto and activate it. The damaged robot learns that a piece of its internal components is the prize at an upcoming Ninja World Tournament and has to work with Hinata and Naruto to make it through the ranks. Of course, Naruto and his mechanical doppelganger don't get along right away, and Mecha-Naruto's jealousy over how the Leaf Village treats the human leads to some drastic actions.
Naruto Shippuden: Ultimate Ninja Storm Revolution's other modes include the standard methods of taking your customized core preset characters out for a spin. You can play in Free Battle Mode in everything from one-off fights to full League style competitions, as well as tournament modes for 4 or 8 players. Meanwhile the Online Battles Menu option lets you take your fighters to Xbox Live and pit them against other people.