Thank you for the question, and for linking to some of my work on infinite chess. You can find additional material on infinite chess on my blog at http://jdh.hamkins.org/tag/infinite-chess/. There are numerous talks, including slides, with infinite chess movies, as well as more detailed research papers and more. I'd be happy to discuss any aspect of that---please go ahead and ask focussed questions about infinite chess.
But in regards to your question, I would agree that most people working on infinite chess are more mathematicians than chess players, and furthermore the central issues seem to be mathematical in nature. Certainly I am more a mathematician than a chess player, although I enjoy a lot of chess (you can play me on ICC, username: JDH).
You ask specifically whether infinite chess has been explored by chess players, as opposed to mathematicians, and the answer to this is yes. My co-author on several of the infinite chess papers, for example, is C. D. A. Evans, US National master, also philosophy PhD candidate at the City University of New York, but not a mathematician. Also, Noam Elkies, professor at Harvard, is also an accomplished chess player who is also a mathematician, and has written on infinite chess.
In my research practice with Cory Evans, I can report that his chess intuition and analysis was invaluable in shooting down and finding flaws in numerous proposed chess positions. But also, it seemed to be an essentially mathematical activity to come up with the various infinite chess positions that illustrate the various high game values and so on. So it was a true collaboration between two fields.