I've wondered about this for some time and here's my take (since I know you want to hear):
Games and art are fundamentally different things. Art is an expression of someone's (or several someone's) ideas about something. Whether it's a story or a painting, it's somebody SHOWING you something. Art is not participatory. The APPRECIATION of art is participatory, but the artwork itself exists without the audience. It may not have any meaning but it still exists.
Games are problems to be solved, where the solution must fit into previously-determined rules. Nobody has to show anybody anything. Nothing has to be said. All that has to happen is the problem (get the puck into the net, capture the king, etc) has to be solved.
People like to watch both. Both are entertaining to a greater or lesser degree.
A role-playing game is a weird mishmash of both. On the one hand, the rules and support materials clearly provide the problem-solving context of a game. However, the fact that the problem being solved isn't always known (a campaign can go in vastly different directions than anyone expects) makes it hard to say firmly that it's strictly a game.
My feeling is that a game session can be art. Sometimes everything comes together, and everyone works in harmony and something fantastic and memorable happens. Sometimes it's just a couple of moments in a game session. But it can be art. There's something being presented (the actions and imagined situation) and there's an audience (the players, who are also the creators).
I always have a hard time expressing this notion. But it's those moments, frankly, that keep me playing.