I used to be pretty active on iccup, and I was a masters-level sc2 player for a while during the beta and when it was first released. So I'm definitely familiar with starcraft and what it takes to become a good player.
I think you're misunderstanding a big part of what is "easy" and "difficult" for humans vs ai. Yes, go is absolutely a more challenging games for humans than starcraft (I also play go, although not very well - currently around ~7k on igs). Starcraft is strategically a much simpler game than go. You are correct in stating that mechanics is what makes starcraft hard for most people, and yes if the computer knew exactly what to do, it would be able to execute it faster and without making any multi-tasking mistakes. But strategy is not what makes starcraft a challenge for ai. Tasks that are trivial for humans can be extremely difficult for ai.
Computers are way better at tree searching than humans, for the obvious reason that they run much faster than brains. So games with relatively small state-spaces, like checkers, are solved quickly. But as you increase the state space, it becomes impossible to search all possible future moves, and this was why go was intractable for such a long time.
The big advancement in alphago is that by using deep learning it is able to evaluate different board-states without doing any search, using a neural net. This allows it to massively prune the search space. Humans are able to do this through "intuition" gained through experience - talk to any advanced go player and ask them about specific moves and they will tell you things like "this shape is bad" or "it felt like this was a point of thinness". AlphaGo was able to gain this "intuition" by training on a massive dataset of go board positions.
In go, the rules are very simple - 19x19 board, each turn you can put a stone in any not-surrounded open space. Its also a turn based game. The state at any given time is fully known. Starcraft is real-time, there are tons of different actions you can take, the actions are not independent (pressing attack does something different if you have a unit selected or not), the game state is not fully known and a given state can mean different things depending on what preceeded it. Not to mention that the search space is massively massively larger. To create a representation of this that can be fed into a neural net and give meaningful results (something like at a given tick, score all possible actions and find the best one) is going to be incredibly difficult. An order of magnitude more difficult than go, imo.