I guess that the similarity of the names come from different places, and in this case might be a remembrance of QuarkXPress. It's convergent evolution! :D
I guessed the name derived as follows: Quarks as the smallest particles, a view in most detail, the building blocks of things. Typesetting as the lowest level of abstraction for creating a document, "down" from Markdown.
People may not know it but at some point in the nineties you'd enter a bookstore and 95%+ of all the books and magazines were typeset using QuarkXPress.
Then Adobe's InDesign showed up in 1999 and things began to change.
FWIW I both wrote and typeset books myself (for a traditional publisher): I did most of them using QuarkXPress but I managed to sneak one I made with LaTeX (it was a hard sell to the publisher / printing press guys who were only ever using QuarkXPress). Also I was forced to heavily modify LaTeX templates to match exactly the one the publisher was using with QuarkXPress.
So yup when I read "Quarkdown is a modern Markdown-based typetting system" the first thing I think about is QuarkXPress: great memories of MacOS (8? then 9?, pre OS X for sure) and my Sony Trinitron monitor.
Was going to ask the same question. Was talking to a friend just 2 days ago who redid all his lecture scripts with quarto and embedded the lecture presentations. Looked neat. Also that quarto interacts well with R studio and jupyter notebooks comes as a big plus.
[0] https://quarto.org/