I picked hobby, but I really think that gaming is both a hobby and entertainment, depending on the game and the level of time invested in it.
WoW is a hobby for me. I spend a lot of time playing and interacting with other players outside of the game on forums, etc. I feel attached to my toon, like I am Naiome...I don't talk about Naiome in 3rd person, because she's the online representation of me. If someone said, "Naiome!" I'd look around to see who was calling my name. Now everyone can call me weird.
I'm also very invested in our guild and the people in it. I think that extension into my real life thoughts and feelings and amount of time I invest in this game make it a hobby.
Other games are entertainment form me. For example, I play Bejeweled or Scrabble on my phone while I'm waiting for the bus, or sing a few songs on Rock Band now and then. I consider that entertainment...something fun I do to pass the time, but I'm not really that invested in it.