i gotta know what typology or game system the mecha protagonists tierlist is referring to, please.
okay so this is a set of recurring character themes ("Arcs") in the tabletop role-playing games of Jenna Moran, including Chuubo's Marvelous Wish-Granting Engine, Glitch, and The Far Roofs. In these games, you decide a storyline for your character to follow, and these determine both specific plot beats that can occur to them, and specific powers that your character gain as a reward/expression of their growth.
Some of these are easier to explain than others. a Role arc is about fulfilling a specified role, a Training arc is about pushing yourself to your limits, but I'm a little shakier on Mystic and Storyteller, which have more idiosyncratic definitions like "this is a story about living in the shadow of a god." i will defer to my oomfs on those. But when the Otherwordly Arc is about receiving strange visions and being transformed by your experiences in another world, yeah that's Hitomi from Escaflowne
My personal recommendation for trying to understand uhhhhh all that stuff is The Far Roofs, which has a draft currently available through BackerKit, but this site is also a very cool and good resource to show links between certain expressions of those Arcs and the powers associated with them