It is possible to play a 1v1v1 (or "3-way free-for-all") match of Starcraft II, with each player playing a completely different "race" with different abilities, strengths and weaknesses. Movement is in real-time rather than turn-based, and the map is comprised of thousands of tiles, while some units can fly, some can burrow underground, and so on.
Unfortunately, 1v1v1 is not all that popular in Starcraft II for the same reason that Clausewitz dismisses 3-way wars in a single sub-chapter of his multi-volume work on war: almost invariably, two players overtly or tacitly ally to crush the third, then settle their own differences as a more traditional 1v1.
http://www.youtube.com/watch?v=mGpeh7dAPrIThe only real way to avoid a quick-dispatch of the weakest is some sort of agreement between all players to temporarily delay that eventuality. It appears to me that the setup of this chess board already incorporates that idea by not allowing adjacent players to jump the two-space "wall" at each border, which is a nice touch.
Here also is an example that goes a step further, a four-player free-for-all, cast by the world's most popular Starcraft II "caster," HuskyStarcraft. If Husky hates FFAs, there's a good reason for it. Once it gets to that level of complexity, the rule actually becomes simpler and more immutable: the first person to attack becomes the instant target for the others (as that player's defenses are necessarily out of position); the person he attacks is the next to go (because he is weakened by the attack of the first), and the one who manages to stay out of combat the longest usually has a walkover to victory while the others weaken themselves, which is widely agreed to be not that much fun, even for the winner.
http://www.youtube.com/watch?v=wzY_AFl9y4Y