The term gamertag become popular when it was introduced with Xbox live. The massive suge in popularity that Xbox 360 recieved resulted in the word going mainstream. A gamertag is nothing more than an online username, something that everyone is already very familiar with. A gamertag is just a specific use for a username within an online network.
While other networks have not officially adopted the term, people still refer to usernames on PSN, Steam and other major network as gamertags.