>> By observing what cards people tend to pick together, you can infer that certain cards have certain properties, even if you never get see the card face.
You're assuming way too much capability that is not present. Just because a human can make this inference, it doesn't mean that a neural net can. Neural networks are notoriously incapable of inference, or anything that requires reasoning.
>> There is no proof that this network has done so, but I think word2vec shows that it's a feasible approach.
Word2vec (word embeddings in general) are actually a good example why this kind of thing doesn't work the way you think it does. A word embedding model represents information about the context in which tokens (words, sentences, etc) are found but it does not, in and of itself, represent the meaning of words. The only reason why we know that words it places in the general vicinity of each other have similar meaning is because we already understand meaning and we can interpret the results. But the model itself does not have anything like "understanding". It only models collocations.
Same thing here. You seem pretty certain that with more data (perhaps with a deeper model) you can represent something that the model doesn't have an internal representation for. But just because the behaviour of the model partially matches the behaviour of a system that does have an internal representation for such a thing, in other words, a human, that doesn't mean that the model also behaves the way it behaves because it models the world in the same way that the human does.
And you can see that very clearly if you try to use a model like the one in the article, or one trained on all the magic drafts ever, to draft a set of cards it hasn't seen before. It should be obvious that such a model would be entirely incapable of doing so. That's because it doesn't represent anything about the characteristics of cards it hasn't seen and so can't handle new cards. A human understands what the cards' characteristics means and so can just pick up and play a new card with little trouble.
As to what I mean by "internal representation"; machine learning models that are trained end-to-end and that are claimed to
learn constituent concepts in the process of learning a target concept
actually have concrete representations of those constituent concepts as part of their structure. For
example, CNNs have internal representations of each layer of features they
learn in the process of classifying an image. Without such an internal reprsentation all you have is some observed behaviour and some vague claims about understanding this or learning that, at which point you can claim anything you like.