Shouldn't I try to maximize the value of my vote given my expectations of the game I'm playing and the people I'm playing with/against? Essentially, I think he's arguing for an idealistic solution instead of a pragmatic one.

He is arguing for a pragmatic solution. He thinks that voting for whom you like has greater chance to help you achieve your political goals than voting for the less disliked major candidate. You can argue that it doesn't work that way (which you didn't), but not that EY didn't use pragmatic reasoning. If his strategy coincides with the idealist strategy, that's, well, only a coincidence.

Essentially my question is, why would you insist that people shouldn't vote strategically, when it is clearly in their best interests to do so? If you strongly believe (for example) Rick Perry would be a threat to your well being, why would you go vote for a third party instead of doing your best to ensure Perry doesn't win?

If you are really convinced that Rick Perry is such a danger that his election should be prevented "at all costs", vote for the strongest of the other candidates. But in most situations, you are not justified in believing such a thing. Your vote has other consequences than only decreasing probability of RP's victory. It also sends a signal to both candidates and influences their behaviour and influences other voters. In most normal conditions the secondary effects have greater value than the primary choice of the election winner because the major candidates are unlikely to implement drastically different policies. (I don't necessarily agree with that, but it is what the original post says.)

I guess I should admit that, in a perfect world, voting for whom you actually want, regardless of perceived popularity, might work well.

Supposing there exists (even as a concept) a perfect world is one of the frequent errors of political thinking.

What should democracy produce, ideally? It should produce election results that closely mirror what people actually want.

This is, in my opinion, a particular example of the problems of perfect-world thinking. You are trying to reform the system to approach some ideal state, where elections reflect what people want. But is this even a coherent ideal? For one thing, different people want different things (and a compromise is usually something nobody is content with). Even one person can have conflicting preferences and be unaware of what they are. I can assure you that voters in proportional voting systems are approximately as dissatisfied with the election results as voters in the plurality systems. I am not saying that all voting systems are equal, but the practical difference is not that big and there is almost certainly no ideal system.

But more importantly, to reform the voting system you first have to grab some political power, either by getting elected yourself or electing a candidate who would support the reform. Do you think that voting "strategically", that is for the less disliked of the two main candidates, would work, when this very candidate would have been elected just because the present voting system is in place (and he probably knows that)?