What is "non-battle" battle anime?

A large part of manga and anime's success in recent years boils down to the simplicity of their approach. Whereas American comics use superheroes—which are essentially power fantasies in primary colors—to explore the life and mind of the protagonist, manga is only concerned with bringing the fight. When manga promises a battle, they more than deliver by providing its audience with dozens of chapters revolving around a specific fight. In American books- I'm starting to feel like Yakov Smirnoff over here- a comic will build to a fight for five issues and feature the pugilistic affair for half of the sixth and final issue. In short, manga has mastered the art of battle.

Manga is so skilled at crafting a confrontation they've even developed a subgenre of battle manga that doesn't lead to a physical struggle. To help explain the concept, here's an excellent video from Super Eye Patch Wolf's YouTube channel that encapsulates the essence of "non-battle" battle manga.