+ As others have mentioned: Brood War is significantly cheaper to run (can be headless, runs well on ancient CPU), making it more amenable to the self-play with massive numbers of games approach
+ Brood War benefits significantly (arguably more than SC2) from skilled micromanagement, which is arguably easier to exploit as it doesn't require long-term/high level planning (but requires a generous actions per minute cap)
+ This API doesn't require the AI to also do simple computer vision/recognition of the game (vs. DeepMind's simplified graphical representation)
+ This API interfaces with game actions directly (BWAPI) vs. mouse/keyboard level actions
It'll be interesting to see which problem (Brood War vs. StarCraft II) gets solved to a compelling degree with learning first.