Think about it this way: the average branching factor of a legal chess move is 35: there are about 35 legal moves that could follow. For Go, the average branching factor is 250. In StarCraft, how many "legal moves" do you have available at a given game state, on average? Tens of thousands? Millions?
By the way, this is made significantly more difficult by SC and LoL not being turn-based games the way Chess is.
And if we're talking about computer playability, the real-time nature of these games cuts both ways; in StarCraft analysis we literally talk about how many "actions per second" a player was able to execute, a field where a computer will naturally have an enormous advantage (part of why I prefer to play Supreme Commander).