Keyless Signature Infrastructures as a secure Post-Quantum Scheme
I would just like to know on what basis they can say it is PQC without any NP problem reduction.


I believe that the point you're making is assuming that a Quantum Computer could solve any problem in NP that's not actually NP-complete quickly (or, at least, in polynomial time).  That's not known to be true; Quantum Computers would be able to solve some problems (such as factorization) in polynomial time, if $P \ne NP$, there's a whole range of problems in NP that's neither P nor NP-complete.