So first, that article is from 2016. Resistance has been known for some time now. There has been resistance with gonorrhea for a long time.
STDs are not the only infections with this issue. Doctors like to prescribe antibiotics for lots of reasons - presumptively, because patients insist on it and doctors just do it because it moves things along, etc. This is a problem, though, because all the antibiotic use when it isn't needed helps create resistance.
I don't think we need to worry that they will become incurable. Doctors are well aware of this issue, and are acting according. You, and other people, can help by not taking antibiotics you don't need, and by finishing all your antibiotics when you are prescribed them, for whatever reason.
Great question.