The key ingredient in a "race to the bottom" is not resource sharing, it's competition combined with a feedback mechanism. Resource sharing figures in a lot of examples, because "consume most of the resources" is a common way to win a competition, but it's not necessary; for example there's no resource being shared in the classic prisoner's dilemma.

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.