I think some people fall into more than one category as well. I know several people that enjoy gaming for the social aspect, even going as far as saying they wouldn't have much (any) social interaction if they hadn't discovered gaming. But they also enjoy other aspects, such strong stories and/or characters.
I view motivation in games kind of like nutrition. You don't go for just one, even if you have a focus. It's about balance while also staying distinct enough in your focus to be meaningful to players.
Posted using Partiko Android