If my understanding is correct, Schnorr converts the integer factorization problem to lattice problems: SVP and CVP. Then he claims he had an efficient algorithm to solve this particular instance of SVP and CVP, thus RSA is destroyed. But, the hardness assumption of SVP and CVP in general is the very foundation that another branch of public-key cryptosystems - lattice-based cryptography - is built upon. So, if Schnorr's claims are true (uncertain and still to be determined), I can't stop to think about its impact on lattice cryptosystems: Can we use the same technique to attack them? I think it's a more important question than RSA [0] - lattice cryptosystems are the candidate for Post-Quantum Cryptography, meant to replace all of the existing public-key cryptosystems of today (e.g. RSA and ECC). Even if the attack is purely theoretical, if it can solve other instances of SVP and CVP, it'll certainly affect the security assessment of lattice-based PQC (e.g. NTRU, also LWE).

Of course, I don't know what I'm talking about.

[0] Factorization had a history of speedups, both theoretical and practical. It doesn't really affect the practical security but always comes at a cost of either decreasing confidence or constantly increasing the keysize, so I won't be too surprised if Schnorr really has new insights to speed it up further. In fact, "We need something with a better security record than RSA" was one of the main arguments for transitioning to ECC - which has already completed at large on today's Internet, RSA is only used for digital signature, almost all key exchanges are ECC now. You can't decrypt post-2016 web traffic by breaking RSA.