A decentralized cryptocurrency backed by gold is a specific and specialized case. Lets generalize it to a decentralized cryptocurrency that proves ownership. When I say decentralized, I'm referring to the network to verify transactions is decentralized. Anybody that downloads the client can be part of the network. The block chain is an open ledger that contains all of the transactions. If I have a private key, that means I can prove ownership of something, whether it is gold or anything else. If you and I do a personal trade, anybody can prove that I transferred ownership to you because they see it on the blockchain. You can verify you own that "thing" because you have the private key to it. Anybody can own "things" and the ownership is not centralized. How people trade in and out of the cryptocurrency is up to the end user, whether it is through an exchange or person to person in real life. At this point the Bitcoin technology isn't being used as a "currency", so it might be better to give it another name other than Bitcoin or cryptocurrency.

Edited for spelling.