I'd also like to add that nearly everything has some aspect of a craft and some aspect of an art. Nearly every task requires some measure of precise repetition and some true innovation. But there are things which are more of one than the other.
For instance, a man is building a chair. He builds the chair by following the procedures he's used to build hundreds of chairs like it. But he carves it a certain way that differentiates it from the other chairs, a carving that he decided he fancied and decided to put in. That's mostly craft, but there was some art to it.
On the other hand, let's say someone is writing a novel. Obviously, there is innovation here in that he, presumably, creates an entirely new story. But there are some obvious craft elements he needs to follow: grammar, contextual structure, the English language, etc. But it's more art than craft.
The act of playing TF2 is more craft than art. Yes, you can innovate by inventing new tactics or thinking of strategies on the fly. But the point of the game is to win in what is, for the most part, a controlled environment. That means that it's inherently solvable, that means there is a system to follow, and that means the perfection of certain skills and attributes, rather than thinking of new ways to kill that Scout running at you, is what is more emphasized.
Compare this to, say, Scribblenauts, which I think is half craft and half art. There are objectives, which must inherently be solved, but the game itself allows you to do it in a nearly infinite number of ways. In other words, you need to do something well, but you're allowed to be as creative as you want to be in going about it.
And compare this to, say, Hell of Sand, which I think is almost entirely art. It's an online flash game that lets you screw around with a bunch of different materials and see what happens. You can create a trail of oil, light it up, and destroy a concrete wall. Or you can create a spout that continuously feeds plants but the plants are on fire, so you get this never-ending loop of fire and plants. It's got some craft elements in that you're ultimately limited in what you can do and thus certain aspects of the game can be mastered, but because there is no ultimate goal the player is allowed to fully express his imagination, so the act of playing it is almost entirely art.
The key differences between these games is that they either have or don't have either emergent gameplay or clear gameplay objectives. TF2 discourages emergent gameplay (in fact, it patches them out) but has clear objectives. Thus, there is ultimately a best way to approach a situation, so it skews towards craft. Hell of Sand has no objective at all, but its very core is emergent gameplay and what things the player creates out of the materials he/she is given, so it skews towards art. Scribblenauts has emergent gameplay with clear goals in mind, so it's clear that you can master a certain way to do things but at the same time you are encouraged to find different ways of doing the same thing, making the act of playing Scribblenauts hard to define.
Of course, this is all talking about the act of playing the game, not making the game. Each of these games are a work of art, but the act of playing them can be interpretted very differently. It's what makes games such a unique medium for art.