This is being discussed in CryptoHack Discord. We are struggling to understand the paper, it is written in a very dense style and the difficulty is compounded by the fact that lattice problems can be a challenging topic even for cryptographers.

Either way, we think that the title "this destroys the RSA cryptosystem" is sensationalistic and probably incorrect. It is presumably based on the fact that the paper claims to reduce some forms of integer factorisation to a lattice problem which can be solved in polynomial time. However, whether this technique applies in the general case to RSA moduli is not argued here and the claim seems to be premature.