With the disclaimer that I'm not an AI programmer either (though I took a few classes in college on the topic); and while I agree with the conclusion that neural network multiplayer game AI is not very feasible, I do think Shamus is wrong on a number of counts, here. The thing he identifies as the problem (needing a network connection) isn't actually a problem and the thing that's actually the problem isn't mentioned.
How Neural Networks Work: (grossly oversimplified and probably mostly wrong)
A neural network is fundamentally just a trained program that takes input and produces output. The term "network" here is probably confusing - it's a program that simulates a network of neurons, but it's not a "network" in the sense of involving multiple machines connected together - so I'm going to avoid it, and just call it a "program", because it essentially is one; it's just a program that was "written" by a different program, not a human.
You start with essentially a random, but fairly simple program with a lot of parameters that can be tweaked (a lot of knobs that can be adjusted to make the program run differently). You run the program with some input, and if it gets a good result, you leave the program alone, if you get a bad result, you fiddle with the knobs in a way that should make the result better. You do this a lot a lot of times, and eventually you get a program that gets good results often (hopefully).
But the program isn't any more complex than it started out; it just has different parameters. So you can easily ship this trained on a user's modest machine and run it, and it doesn't need any sort of network connection to run. So, assuming you could train a neural network to play Civ, then it'd be runnable on the users machine without needing to "phone home".
The problem, though, is the training. You can only train a program if you can algorithmically determine if the result of a given run of the program was good or bad. That's trivial for things like identifying hats in photographs. You collect a dataset of photographs that you know either have a hat or don't, and then give those to the program to see if it gets it right.
This is possible for some single-player games. The original question asker is probably thinking of something like MarI/O (which does a good job explaining neural networks) when they mention AI training to play video games. That AI is trained by using how far (and how fast) Mario gets to the right as the metric for evaluating how good the program did.
A multiplayer game is much harder. You can't just feed the program a position in Civ and check if it produces the "right"?set of moves, because there's no "correct" outcome, and it's a rather tricky subjective problem to determine whether a given move in a given position is helpful for winning or not. And games that aren't turn based are going to be even worse.
You could, however, train a neural network AI to imitate how humans play the game. That turns the problem from something subjective ("is this move good?") to something objective ("is this the move that the player actually made?"). But, to do that, you need do need a lot of historical data. So it's a chicken-egg problem: you need an AI to ship the game, but you need data from people playing the game to write an AI for it.
You could write a traditional AI, ship the game, collect data, train an AI against that data, then patch the trained AI into the game, but that's a ton of effort for not a lot of benefit: if Civ V's AI suddenly got better 6 months after launch, would that really bring in enough revenue to justify the expenditure?
Multiple Difficulty Levels:
You could, with enough data, overcome the difficulty thing that Shamus mentions. Instead of feeding all the data to train a single program, you train multiple programs by giving different parts of the data to each program. If you want to make a good AI train it against the moves that cause a player to win the game, to make a human-like bad AI, train it with the moves that cause the player to lose the game. (And some combination to make various levels in-between. Or use an ELO system and train it that way)
Another downside is that neural network AI are pretty fragile if the problem changes. If you initially train your network to identify bandannas as hats, and you change your mind and decide that they aren't hats, you probably have to retrain your network from scratch. A significant game patch (much less an expansion pack) could completely break your AI, unlike traditional AIs which are much easier to tweak.
And you would need the game to "phone home" to collect historical data; some players won't like the game gathering info (though I'd guess many of them just aren't telling you that they do it already) but unlike Shamus's scenario, the game won't stop working if it can't phone home, since the data collection isn't a core part of running the game.