Well, various nations have had trade wars for a long time. Country A exports something to Country B, A gets upset when B uses import bans or tariffs to prop up its domestic industry or simply keep things out, and then A retaliates by limiting imports from B or worse. Eventually the two countries learn to do without, or they resolve their differences, hopefully peacefully, sometimes violently.
What we're seeing now is a system in which trade treaties are becoming massively multilateral, treaties are tangled up together for mutual support, and international bodies are set up to administer them. It's still possible to pursue national interests over international trade, and to engage in trade wars, but it's become a great deal harder by design.
I agree that we need to push for more national sovereignty, so that trade is managed by politically accountable, democratic institutions, rather than potentially dangerous IGOs, but it's probably worth remembering that we pushed as hard for this mess as anyone, and now we're getting a taste of our just desserts.
As for this particular situation of course, it might've happened the same way regardless. Copyrights are strictly national in nature. US copyrights are only good in the US, UK copyrights only in the UK, and so forth. Most works have many separate copyrights attached to them. Treaties between various countries mandate that when a work receives a copyright in one eligible country, all the others grant copyrights for that same work too. Antigua and Barbuda only grant copyrights to US-originating works out of this sort of reciprocity, and can cease to do so as they see fit, including as part of a trade war on unrelated matters, since this might give them some leverage.