The fine headline is leaping to quite a conclusion.
I was able to try reading the actual paper this time. It's a bit dense for me but whatever. It's a meta-analysis. The authors didn't actually grow any plants but consolidated results from many other papers. So far, so good. This is a normal research process.
From the quoted summary, it finds a 3.2% decrease in minerals in major crop plants. That seems a small effect to me, likely overwhelmed by other factors. For example, if you were living on 1500 calories a day 30 years ago and now get 2000, I'm going to go out on a limb and say you're likely to be healthier even if each individual bean is less nutritious.
There's also a lot of other things going on. I couldn't follow their methodology well enough but I wonder about confounding factors. For example, were they comparing the same strains of crops? Seed companies come out with new varieties all the time and it wouldn't surprise me if that has a much larger effect on nutrition than CO2.
In summary: interesting research. I'll take their word they found a real effect. I'm not at all alarmed because I expect there are much larger changes at play.