Shogi, chess and Go are "perfect information games", meaning you can see the whole game state. It's a whole different thing to be able to solve games where you don't see everything (based on uncertainty).
A big class of imperfect information games can be modeled by having a record of everything the agent has seen so far. Then it has exactly the same, if not more, information available than a human player in the same position. We know that with equal information AIs can make better decisions than humans (see also, AlphaGo :] ) so at that point the AI could reasonably be expected to achieve superhuman performance.
The "imperfect information games are harder for AI" crowd are going to be surprised by just how badly humans deal with imperfect information. AIs have a much better memory than humans do, and much more potential to use actual probability which humans are truly shocking at utilising (although neural networks don't seem to utilise this edge; so far).
Earlier this year, DeepStack, a system combining neural nets with search, competed live against humans without any side being dominant. Search policy guided training might improve its results, which are impressive compared to even 5 years ago, but this highlights how much more demanding imperfect information games are.
Actually machines can have an even higher advantage in those cases, because they can be much better at estimating probabilities than humans. Think of card counting, for example.
Furthermore, techniques like monte-carlo tree search used in AlphaGo don't work very well for poker - You can't just try and find the "best move" from the current game state, or you will end up playing a highly-exploitable strategy. You essentially have to solve the entire game every time (or completely in advance) to make sure you are playing a balanced strategy.
Only the Counter-Factual Regret Minimization algorithm has been able to achieve this level of play in Heads Up, and right now it looks hard to scale to poker games with more players, like the full-ring games you see at the World Series of Poker, for example. We still have a ways to go in Poker AI.