As an 87% Explorer myself, I think "loyalty to an environment" might be a closer fit than "loyalty to a vision". I want to get invested in a game world -- its lore, its inhabitants, and the many different places that it comprises. I like finding hidden places that most people would never see. There's no particular vision here; in fact, I spent quite a lot of time in World of Warcraft hunting for ways into the geography _between_ zones, which had all kinds of messed up terrain that was clearly not envisioned in any sense. And when the prospect arose of flying mounts allowing anyone to explore the interstitial spaces of Azeroth, that meant the developers would have to cover over all those special places I enjoyed. The devs certainly had a vision, but I felt no particular loyalty to it.
A fun discussion on characterizing the motivations of gamers is "Engines of Play: How Player Motivation Changes over Time" [1]. I'm not hugely in love with the sorts of models, he builds, but any sort of structure is useful for kickstarting your thought.
The big win in that talk, though, was that he introduced me to Self-Determination Theory[2]. A very convincing theory on motivation. It's introduced in the talk at 38:05.
[1]: https://www.gdcvault.com/play/1023329/Engines-of-Play-How-Pl... [2]: https://en.wikipedia.org/wiki/Self-determination_theory
The types are achievers (people who want the highest score), explorers (people who want to understand the game world), socializers (people who are there to hang out with other people), and killers (competitive types who aren't satisfied with winning unless someone else loses).
"Loyalty to a social group" sounds like socializers. "Loyalty to a person" could also be characteristic of socializers. "Loyalty to a vision" is absent from Bartle's types, presumably because people generally view games as entertainment and don't look for meaning in them the same way they look for meaning from work. "Money and perks" seems kind of similar to achievers, or to killers if their primary motivation is not just to obtain wealth for their own necessity or enjoyment but rather to gain more wealth than their peers.
Bartle's explorer type doesn't seem to have a clear equivalent, unless one considers the pursuit of knowledge to be one form of loyalty to a vision.
[1] https://en.wikipedia.org/wiki/Bartle_taxonomy_of_player_type...