Just saw this thread! I'm a pyrographer (I burn stuff ), and I don't think this one was burned, though it's a little blurry - for instance, at the top there's a tiny semicircle missing from a symbol. Pyrography would be pretty hard to damage so precisely.
You could definitely burn this kind of design in, though - I've done similar ones using the spoon (shading) point of this machine: Link. However, might be hard to do if you've already made the space for inserts.
Anyway, great project - looking forward to seeing the finished version. </End silly woodburning diatribe>