There have been many attempts at creating a taxonomy of gamers. The Ur-attempt was Bartle's Taxonomy of Gamers: https://www.youtube.com/watch?v=yxpW2ltDNow which people have been refining or reacting to ever since. Knowing the name Bartle helps you delve into the prior art and see what people have fleshed out in this arena.

On a slightly different path, John Boyd is the intellectual progenitor of at least one school of thought into how to make organizations more game-like in positive ways through his observe, orient, decide, and act (OODA) Loop. Knowing the name Boyd and OODA can help you think about the meta-game properties of the organization and your role as a manager cum game designer.