Go's game state, for example, is very small. You can pretty much represent it with a 19x19 array of 2-bit variables, because each space only has three possible states. That's only 722 bits. Maybe a few more to track whose turn it is and how many pieces each player has remaining.
In contrast, Starcraft can have hundreds of units in play from dozens of types, each of which usually has at least a position value (x and y) and a health value, and commonly has other things like energy value and cooldown values. And each of these you'd need at least a 16-bit int. And that doesn't even get into the enormously larger possible action space for each "turn".
Could you explain how you figure that in more detail?
I mean, to my untrained eye, it sounds like it wouldn't be so, since in every time slice of the game (equiv. of a turn in Go?) you can have hundreds of points of control - hundreds of levers to choose to pull - and of course that's in every frame (or whatever interval the UI actually allows you input).