The article is blurring the right to attempt to manufacture without legal restriction, and the ability to successfully replicate the formulation. This blurring makes sense from some points of view (especially from Jacobin's POV, and from an argument of immediate justice for the most people), but obviously falls apart from other POVs.
I assume poorer countries are not doing this due to fear of foreign aid being withdrawn, but this isn't really an issue of "rights".
Jacobin's point is that the pledge is meaningless because the patent lacks sufficient information to make the vaccine anyways - it's all locked up in trade secrets. Jacobin then frames this in terms of rights.
Jacobin claims that the way patents are usually discussed will imply that patents are about 'positive rights' - that is, if you have a patent or license, then you have the ability to commercialize (or whatever) the thing that is patented. Jacobin then claims that in reality, patents are just a negative right. Having a patent, or a license to a patent is just a freedom from not being sued for commercializing a product - since the real positive right that people want - the ability to successfully produce the object is actually wrapped under trade-secrets. The article is basically arguing that this split is injust, or at least extremely misleading, and is trying to call out the bullshit.