Like I said the research is equivocal. From the study you listed: "Although it is evident that high-intensity interval training is beneficial for endurance athletes, effects of traditional resistance training have been less conclusive." And then they go on to show that combining explosive resistance training with high intensity intervals on the bike is beneficial. Well that's not really surprising given that every study looking at interval training shows improvement. It's not clear what role the resistance training had on the improvements.

The point is that it appears much more difficult to definitively show that weight lifting improves cycling. Certainly, some people (including older men) are strength limited and can benefit from some amount of strength training. There are lots of riders, however, who are not strength limited and for these riders weightlifting provides little or no benefit.