The things he is talking about in the book is bluffing and psychological warfare.

That may be, but you said:

If we only learn about how to win competitive games, then we have fewer tools for dealing with cooperative situations

Which, to me, is about more than just bluffing and psychological warfare.

Are these useful skills when trying get something done cooperatively or do they harm the process if used?

I don't know. I could easily imagine the answer being both, depending on circumstance, thus making as simple a characterization of them as you seem to implying pretty difficult.

Possibly we mean different things by cooperative situations. I'm talking about situations where people have to work together to win, you can't just wipe out or ignore everyone else. This means balancing your goals with others

This makes the point that cooperative scenarios are harder than purely competitive scenarios, not that we're particularly bad at them. "Balancing your goals with others" is in the end just another way of saying that your goals positively correlate with theirs. Most big problems (and yes, even Magic) contain agents with goals both positively and negatively correlated with yours, so "cooperative or competitive" is not, in general, a binary proposition. Do you think we're particularly bad at planning in the presence of others with positively correlated goals?

You can treat solving global warming as having competitive elements, but then you will be less efficient at actually solving the problem by having to spend resources on competing, which could have been used for solving the problem.

If it has competitive elements, then I certainly want to treat it as though it has competitive elements, regardless of my final strategy. But you also seem to be suggesting that approaching an objective competitively is inherently less efficient than approaching it cooperatively. Surely you don't mean that.