There are problems with definition here.
A Ponzi scheme is a fraud where the operator lies about the source of the funds he uses to pay his investors their promised return. Instead of trading he simply pays old investors with new investors money.
A "ponzi game" of rounds based on this principle, where everyone is aware that at the end of a round some people will be paid and some won't, is something totally different, BUT
It still has potential to be a fraud because there is no transparency about the owner of the early money, which could well belong to the operator.
Until there is some sort of equivalent to dice's "provably fair" for these games then they should be treated as scams just like "conventional" Ponzis.