Well, "strong AI" is really more of a philosophical question than a technical one. You may "believe" in it and choose to apply that believe to AIW, but it's not really something you can prove.
Certainly.
It's very possible I just didn't know / don't know what I'm doing
Sure, no worries.
At a tactical level, AIW is very RPS-ish. Fighter>Bomber>Frigate>Fighter (I think). The fact that the AI apparently doesn't pick a force mixture based on the player's current force mixture means that you've basically decided on a random strategy for the AI force mix -- which can force the player into a tactical tie, just like a random strategy in RPS can. (Unless the AI picks a non-random force mixture that isn't responsive to the player force mixture, in which case the AI is doomed to a tactical loss position over time.) This is probably a good decision, since a human might be better at adapting to a co-adapting enemy force mixture than the AI would be. On the other hand, you may want to look at some of the algorithms of the winners of the International RoShamBo Programming Competition (http://webdocs.cs.ualberta.ca/~darse/rsbpc.html). I think I remember reading that these programs could regularly beat humans at RPS tournaments.
Yes, there are a huge amount of RPS relationships, and the AI does not choose its ship mixes. However, it's vastly more complex than even Rock-Paper-Scissors-Lizard-Spock, in that there are dozens of interrelationships. The AI generally tries to keep something of a balanced force on its own planets, and then the human players have the "tempo" (in the Chess sense) to treat this as a puzzle of sorts to solve. If the AI was always adjusting its ship mixes versus your ship mix adjustments, I think that would lead to the only valid strategy for human players being to keep a super-broad array of ships in every mix. As it is that is sort of the case already, but that is mitigated somewhat by the AI being more of a specialist at each wave and guard post, and thus the player having some opportunity to specialize in response to those.
I guess the main thing is that the AI is acting here both as a scenario generator and as an opponent, and ship mixes are completely about scenario instead of trying to beat you. For every reaction there is an equal and opposite one, and if the AI were more pointed and sneaky with its ship mixes, then the human players would not get to be. As it stands, the AI is intentionally not, and so the players get to be a bit. I guess my main goal in general with the AI in AI War is not to win and kill the humans immediately, but rather to provide the widest variety of interesting and challenging situations possible. To that end, certain sorts of superfast analysis I keep out of the hands of the AI. On the other side, in tactical engagements where the ships are already set and known, I let it work in an unbridled fashion (assuming a high enough difficulty level). So that gives really a hybrid mix, where the AI is trying to beat you and where it is just trying to set up an interesting scenario; in many ways, the AI Director in Left 4 Dead does a lot of the same sort of thing -- in its case, it is more about mood and tempo and atmosphere than just trying to kill you (when it populates zombies), but the zombies themselves act out of a sole desire to kill you as fast as possible. Sort of the same idea in AI War, although I hadn't played L4D until well after AI War was released (I had read articles, though, and they were something of an inspiration).