What does "a 15360-bit RSA key is the equivalent to a 256-bit symmetric key" mean?
The statement 


  a 15360-bit RSA key is the equivalent to a 256-bit symmetric key


does not take into account quantum algorithms. In fact, it is based on a specific computation model. 

It is just based on the fact that there exist sub-exponential algorithms for factoring and therefore you need longer keys than when using symmetric-key crypto where it is believed that there is no attack that is more efficient than exhaustive search.

I'm not 100% sure, but I think the NIST standard is based on a paper by Lenstra and Verheul (PDF).