Certainly. Why wouldn't it be considered as money? It has value and is used to exchange for other goods and services, just like paper money, only it is digital!
People have different understanding but what is right is the government definition because they create money. Even if it's not on the definition but by looking on what we are holding we can already consider it as money, bitcoin is money for me.
Strictly speaking, in technical terms, it is called cryptocurrency. But the root word is still currency. And a currency's role is as an instrument to purchase something or pay some services. 
