Their main point is at the end:
> Banning plastic straws is stupid.
They're probably right that throwing out plastic straws is better than throwing them in the recycling, assuming that plastic straws can't be efficiently recycled. That being said, many US recycling utilities typically sort the recycling on shore, and plastics that are too small to be efficiently identified and recycled (such as straws and loose bottle caps) will just be sent to the landfill regardless. How recycling is processed differs a lot across the country, so it's hard to make generalizations.
But that doesn't support their final conclusion about whether plastic straws should be banned. The author doesn't give a reason, but implicitly that they think paper straws suck, and must suck. Which a lot of the ones today do. But it's an odd hill to die on, given that basically all straws before 1960 were made of paper. Their ire should probably be directed at the establishments they frequent for buying cheap and terrible paper straws instead of spending a bit more to get good quality paper straws. Such companies probably want to get you pissed off by paper straws to demand that your government remind the ban so they can go back to using cheaper plastic straws.