I wish I had been in the chatroom for this.
On defining "art", I generally agree with Scott McCloud. His definition is extremely broad and encompasses any activity that humans do that isn't directly related to survival or reproduction (although I think you can take it further and eliminate a lot of the aspects of reproduction, just not the instinct... some people are artists in bed...)
He drew a comic to illustrate this. The first page had a caveman looking to catch and procreate with a female (reproduction), but is interrupted by a sabertooth cat which he runs away from (survival). Here's the second page:

At this point I have to plug his book, Understanding Comics, which is one of the greatest books ever written and applicable to pretty much all things creative, not just comics.
The little segment with the cave paintings illustrates why art is so great. Some caveman was 'arting', just dicking around and realized that he could make marks on a wall that resembled whatever, and then used that new knowledge to draw a tutorial on killing buffalo, or used it to draw some significant event that he remembered from the previous week. Either way, if those images were meant to be practical, then those paintings are literally the most significant bit of human history we have, as that's the oldest 'written' history or store of knowledge. All cause some caveman was dicking around with a bit of charred stick on a wall.
My issue with videogames is more to do with story, in that games aren't inherently a storytelling medium, they're a story creating medium that people are trying to use to tell their stories.
People didn't play Pacman or Joust because they had amazing stories, but those games did have stories that you created while you played them. They had a beginning when you put a quarter into the machine, a middle while you were playing the game and an ending when you either beat the game or (more likely) ran out of quarters or just decided you didn't like the game. Based on that story, you decided whether you'd ever go back and play that game again, or whether you'd go try a different one. The novelty of games is that the experience you have is different every time you play it (ideally). The rules and mechanics are the same every time you play PacMan, but the game will be different every time you play it.
Modern games have that going for them, but they're no longer that pure. Games have evolved into these interactive movies where the goal is no longer to have an experience based around some mechanics, but to experience a series of events and have some level of control in how things play out. On the other hand, sandbox games like GTA4 and Skyrim are heading in what I feel is the correct direction, but are still trying to crowbar that modern gaming "experience the excitement of playing an epic film" philosophy in there.
To elaborate a little on what Trey said, there's more parallels to be drawn between early films and gaming. The earliest films were just spectacle and amusement. The first games were pretty much that as well. Then movies started telling stories, but they mostly used stage techniques cause that's how you did that story telling thing with actors, right? Then they started using editing and the camera to do things that you couldn't do on a stage, but most of what you did with a movie you could do on a stage. I think that's where games are right now. They're basically making movies, but putting little interactive things in there that only a game can do, but you could make a Mass Effect movie because that's what a lot of that game's storytelling elements are.
When we get to a point in games where you can no longer make the game into a movie and do it justice, that's when games will have come into their own. I think the earliest movies did that perfectly, but purely as a "look at what we can do" sort of way. You couldn't make "Humorous phases of funny faces" a stage production. You couldn't really make Tetris or Donkey Kong into movies because the novelty of them is how videogamey they are. They are purely videogames. In another 30 years we'll probably be at a point where videogames have gone back to those fundamental ideas to tell stories that are uniquely tellable only on the terms of games - probably having to do more with your own personal preferences over how you'd like the story to go, rather than how some guy at EA decided it should.
If you're interested in games that make my dick hard, check out X³, which is a space combat / trading / etc game. You get a space ship or two and a little money and a massive universe and that's the game. There are missions and stuff, but you don't have to do them, and in fact I would recommend not doing them. Just flying around and exploring the world is worth it. It's one of those games where there's a ton of stuff to do and you can play the game however you want. You can be a good guy or a bad guy or an innocent bystander.
Or check out Dwarf Fortress. Or check out any game that has some sort of random mission generator or sandbox mode like Sim City or IL2 or ArmA 2. Check out Tower Climb if you just wanna play a simple 2D game. Check out The Binding of Isaac, a game that has a bit of story but fits that onto a totally random game. Skyrim is a great game to explore in as well, although that's pretty much all you can do if you don't do at least some of the missions. You have to unlock a few things before you're free to just play the game however you want, and even then you can tell that that's not how the game was meant to be played.
Also, I love longplays and let's plays. The best collection of longplays on youtube is here:
http://www.youtube.com/user/cubex55?feature=g-user-u
Those guys upload everything from modern games to old 1980's arcade games and everything in between. No talking or commentary whatsoever. Just the games.