I don't know what was originally in Satoshi's head but now this idea has developed into a successful alternative to fiat.
He wanted to build the "peer-to-peer electronic cash system" : the whitepaper of bitcoin says it clearly. The system that is similar to physical cash, but with the ability of being transfered via Internet. Although these idea and realizaton were very ingenious, the creator of it could still underestimate the significance of his invention, it was impossible to predict that bitcoin could become the replacement of current monetary system and would start changing people's minds on how the system should really work.
I would say, it is not an alternative to fiat, but perfectly functioning system that is intended to replace it completely, the system that shows all the drawbacks of current monetary system and gives a solution at the same time.
