Hello, I love this topic. The hobby lacks a common terminology. Worst : the same words mean precise different things in various parts of the community. In fact, we don't have a community to speak of. There's a lack of overarching authority, academic or otherwise. And that's probably good : existing authorities are closely linked to specific games and scenes. The most useful framework for the hobby I have found is socio-cultural rather than academic.
That means there are lots of *ad hoc*, local theoretical patches rather than an unified theory. Larger scale theories can inform you about the market and generally unexploited areas. But smaller scale theory tells you what can happen at the table, with a specific "type" of player group, with ultra-specific socio-cultural references. That may be harder to think but that's not nothing. That's where we do most of our design and play.
In practice, I've never found it impossible to discuss advanced design or play with everyday words, and a few technical terms linked to a few key articles (agency, alibi, spotlight sharing, input randomness, etc.) Most of the time, it has proven more helpful to give a general indication, examples, and kick the mind reeling in a new landscape, rather than build a framework out of "cloud elephants on a golden string".