A simple game that this architecture would fail at is Simon [0], where you are presented a sequence and then are tasked to replay the sequence.
There's a lot that suggests that humans and machine learning algorithms learn in very different ways. For instance, by the time a human can master a game like Go they can also perform image processing, speech recognition, handwriten digit recognition, word-sense disambiguation and other similar cognitive tasks. Machine learning algorithms can only do one of those things at a time. A system trained to do image processing might do it well, but it won't be able to go from recognising images to recognising the senses of words in a text without new training, and not without the new training clobbering the previous training.
To make it perfectly clear: I'm talking about separate instances of possibly the same algorithm, trained on a different task every time. I'm not saying that CNNs can't do speech recognition because they're good at image processing. I'm saying that an instance of a CNN that's learned to tag images must be trained on different data in a different time if you also want it to do word-sense disambiguation.
And that that is a limitation, that stands in the way of machine learning algorithms achieving general intelligence.
A human brain (or any other animal brain for that matter) is almost infinitely more advanced and computationally efficient than state of the art machine intelligence, even without taking things like thoughts, emotions and dreams - which we currently do not understand at all - into account.
It's a huge accomplishment for machines to be able to win over humans in games like chess and go and <insert game here>, but these are games originally designed for humans - by humans - to be played recreationally and I think we shouldn't read too much into it.
Look, there's no doubt that computers can outperform humans in specific tasks. There's no doubt that AlphaGo is intelligent when it comes to Go, but on the other hand it would be completely incapable of tackling a different congitive task- say, language, or vision, or discriminating between say two species of animal [Edit, since there seems to be confusion on this: you'd need different training data and another training session to perform well at a different task].
That's a limitation of our current systems. They generalise badly, or they don't model their domain very well. You have to train them again for each different task that you want them to undertake and their high performance in one task does not necessarily translate in high performance in another task.
Humans on the other hand are good at generalising, which does seem to be necessary for general intelligence. If we learn to play a board game, we can take the lessons from it and apply them in, I don't know, business. If we learn maths, we can then use the knowledge [Edit: of what constitutes a well-formed theory] to tackle physics and chemistry. And so on.
So, let's say that "true AI" is something that can show an ability to generalise from one domain to another, like humans do, and can be trained in multiple cognitive tasks at the same time. If we can do that, then computers will already be super-human, because they can already outperform us in terms of speed and precision.