Unfortunately game situations are magnitudes more complex than the single problem of telling one handily pictured husky from another (which if ever needed as a 'tool' takes up a good sized NN by itself, and then we will need the 10000 other 'tools' (and their training sets) for all the other classification/differentiator/deobfuscator tasks, and then the processing resources to run them ALL in a timely manner.
Maybe if you were using NN to spot 20 year old game pixel patterns for game objects in a clutter of on-screen scenery this would be relevant. Unfortunately that IS still just a basic sensor filtering task and does little for the rest of the problem of playing the game.
"They can translate sentences between any two languages, with very little additional machinery."
I'd like to see the project that claims THAT. Particularly with your use of the word 'any' - when there are so many world languages to map between and more than a few that dont have exact translations of certain words/idiom-contexts with other languages. (English:"The spirit is willing but the flesh is weak" --> Russian:"The wine is good but the meat is rotten"...)
Text to text NN input ??? or again you are claiming some subtool NN of a much more complex program and data set (dictionaries/grammar rule translators) where the NN component actually turns out to be a trivial part of the whole thing. ???
Temporal cause and effect pattern spotting has major difficulties with noise from nonrelevant situational factors and a further combinatoric explosion of endcases, some coming now from irregular event timings. Again in more complex simulation environments this forces greater human intervention being required in the training (hand training the logic which otherwise could simply further just be built as conventional logic) which is the most significant chokepoint of complex NN solutions.
For Go I could see use of convolutional neural networks to convert the simple Go grid into higher and higher level features and trying to spot the needed decision patterns . How well can the future-assessment be evaluated - training the NN effectively for that generalizing, without it having terrible gaps? But again that is for an example of a game with 'situation' that is utterly flattened out/narrowed in detail complexity, compared to just about all other 'games'.