For go modeling basically you have in input an image of the go board, and for DOTA an image of your screen and the action you have are "limited" and do not change wildly depending of the state of your screen (except if you're dead on Dota).
For Magic, you can't just use deep reinforcement learning with an image input, you need to somehow track the state of your deck, cards, instant effects, what your opponent did ...
This article is all about how those synergies are Turing complete and thus cannot be easily calculated since doing so reduces down to solving the halting problem.
edit: that being said I suspect that writing an AI that plays "well enough" to beat human players, as opposed to optimally, is quite doable.