I am starting to believe the problem is hardware overheat: had a relatively
long session with the PC case open and no incident. Can it be considered a bug?
Is overheat prevention a tractable issue in software?

Anyway, I tried to run with R600_DEBUG=ps,vs,gs, but I am not sure how to
retrieve the information you need. I have the game from Steam, I ran it by
typing in the terminal:

$ export R600_DEBUG=ps,vs,gs
$ steam -applaunch 220200

And it output to the terminal the usual, nothing specific to Mesa.