It seems the idea is that you could pack people in for the few-hour journey to the Cycler, and the departing journey once you get to Mars, and give them more space and shielding during the voyage. But that all requires that a large, spacious, well-shielded Cycler is already in place. This is all covered in the article, but just as an interesting aside rather than a massive impediment to the utility of such a piece of infrastructure.
All of this is such a distant problem, it seems way too soon to even speculate on. We're hundreds of years away from the logistics of transporting thousands of humans to Mars being a practical consideration. As such, the mere mention of Starship feels utterly anachronistic. Even if you think colonizing Mars is a good idea, wasting time thinking about problems for the year 2300 is not the best use of your time.
(The article is from 2021 by the way.)