I agreed with everything you said until here. Developing good representations of state is precisely what today's machine learning is so good at. This is the key contribution of deep learning.
You seem to be supposing that a human expert is going to be carefully designing a set of variables to track, and in doing so conveying what features of the input to pay attention to and what can be ignored. Presumably the ML can then handle figuring out the optimal action to take in response to those variables.
I think it's much more likely to be the other way around. ML is really good at taking high dimensional input with lots of noise and figuring out to map that to meaningful (to it, if not to us) high-level variables. In other words, modern AI is good at perception.
What it's significantly less good at compared to humans is what might formally be called the policy problem. Given high level variables that describe the situation, what's the best course of action? This involves planning. We think of it in terms of breaking the problem into sub-objectives, considering possible courses of action, decomposing a high level plan into a sequence of directly executable actions, etc. AIs might "think" of this problem in different terms than these, but it seems like it still has to do this kind of work if it is going to have a chance to succeed.
We don't have obvious ways to model this part of the problem. For the perception/representation building problem, I can almost guarantee the solution is going to be a ConvNet to process individual frames combined with a recurrent layer to track state over time. On the other hand, I'm seeing some plausible solutions to the policy problem emerging in the literature, but it's still very much an open question what will emerge as the go-to. In AlphaGo, this part of the problem is where they brought in non-ML algorithmic solutions like Monte Carlo tree search, and one of the reasons StarCraft is interesting compared to Go is that those algorithmic solutions are harder to apply.