Mind you, we're currently assuming that both axes are cut in one stamp. This might not be the case for a production line process.
A simple puzzle where corners of each piece meet (ie no joins in the middle of a straight side of another piece) could be manufactured on a conveyor, passing under two rollers - one for cutting the "vertical" joins and one for cutting the "horizontal" joins.
Having said that, I do think that they are most likely to be stamped out. For the reason that joins do often occur in the middle of the sides of other pieces.
Another possible scenario might be a modular press, set up something similar to a printing press. i.e. you have thousands of cutters that correspond to only one side of one piece, and they are mounted on a base plate in a particular configuration for a stamping run.
I've fired off an email to Hasbro's media contact people asking if they've any information or if they can point me towards manufacturers of press machinery. Will see if anything comes back... (Hasbro own Waddingtons now, it seems).
cheers Richard
-- Richard Sampson
email me at richard at olifant d-ot co do-t uk