Not necessarily, it's also "barter-system-like". It is only Ponzi-like if the funds that have to be paid to the inverstors are necessarily higher (or of more value, if they're non-monetary) than the investments of the investors. According to your definition, every barter system (LETS) which is not backed by fiat is also a Ponzi (If you should claim that e.g. time banks are different because there seems to be a guarantee for a certain value measured in time - they aren't, because nobody is forced to accept the time bank currency, so exactly the same risks apply as in Bitcoin.)

They do pay a non-monetary value, "hashrate", which translates into network security and thus adds value to the network. And that's the point of Satoshi's proof-of-work model.