In bridge, can the "rule of 20" be used outside of opening bids (e.g for takeout doubles)?
What North and South did is not a take out double, but a conventional response to a strong club opening.

One of the most important things to do facing a strong club is to intervene, making it more difficult for the opposing side to reach the optimum contract. You don't want you opponents to relay themselves into a hard to bid (grand)slam that no one else will make.

One of the simplest defenses to a strong club is Mathe, where Double shows the majors, and 1NT shows the minors. This is the easiest way to convoy shape, so your partner knows where to intervene, or where to sacrifice.

In this particular auction it would probably be better for South to bid 1D asking for North's better major as South has no real preference, and North would be 1S.