Also once the US can manage to get 130 countries to agree to its tax regime in one area, guaranteed it won't stop there.
I'd say that this however is not a resource sharing situation. It's a competition for the magical money tree of corporation taxes. And that's a good thing, because "setting up an environment in which businesses cannot thrive" is often a vote winner, but is a terrible idea.
Anyway, you're right that this a competition for corp tax money, and that it could be bad in theory if there was no competition for it, since e.g. we could all collectively agree to set the corp tax rate too high, which I agree would be bad. But there's no ratchet effect. All we have to do to avoid the "taxes too high" problem is be aware of it and decide not to do that, whereas we cannot avoid the "race to the bottom" problem by being aware of it, we need an agreement like the one described in the article.
This method contains no incentives to do it (competition) and no way to establish what is "too high" (also competition).
Imagine you and I are neighboring farmers who irrigate our fields from the same river. Our farms grow, as does our water use, until we're each using half the water. I buy a bigger water pump and start sucking up most of the water, leaving you with dying crops. So you go out and buy an even bigger pump; now you're getting most of the water, and some of my crops are dying.
What's the result? There are only two outcomes here: either we agree to split the water, or we spend more and more money on larger and larger pumps until neither of us has any profit left over. The latter outcome is the "trap" - neither of us wants to spend every spare dollar on pumps, but unless we come up with some agreement, that's what will happen.