Let's set aside the fact that, for many people playing Roleplaying Games, particularly, though not exclusively, D&D, the game is the point, with the role-playing as the pleasant addition.
When comparing a roleplaying game to a roleplaying activity, the game provides a much broader mechanism for conflict, and conflict is at the center of most fiction. This isn't to say that we can't have conflict in an unstructured roleplaying activity — conflict resolution courses are built around roleplay. But conflict resolution activities are limited to verbal conflict, and they rely upon the ability of the participants to sustain and resolve that verbal conflict, which, for some people, could be difficult. That being said, they can be quite fun. I quite enjoy conflict resolution workshops. Roleplay a conflict between on the condominium board about putting in a ductless air conditioning system. It's a blast, honestly!
Still, the game allows us to bring in mechanics for dealing with all sorts of conflicts that we can't directly act out. Role playing a fist fight stops being role play, unless you plan to actually hit each other; otherwise, you need to be stepping outside of your characters constantly to choreograph a fight.
And, of course, the mechanical imperatives of the game provide plenty of inspiration off of which to build ones role-play. This is why I enjoy building characters by rolling offer a series of charts — the unexpected inputs I get from the dice help me to think outside the box a little bit and rationalize something I would never have come up with on my own.