Is Mathematics or Computer Science more important for a career in cryptography
This question can be closed because the answers are opinion based. Nevertheless...

It depends. It does not look like they are going to design essentially new algorithms for encryption, signature, voting, etc. They have focus rather on applied aspects. In particular, they expect you to study and evaluate cryptographic algorithms and protocols of specific hardware and software. To be able to do that you definitely need skills in computer science.

Why are you asking about data structures particularly? It is a small topic compared to the others. Yes you should learn it, not because of this job, but because otherwise you will not be able to program.

To your questions: Yes, programming skills are important for this type of job.

Which topics are relevant? For this job following topics seem to be relevant:


Cryptography (of course)
Number theory
Programming
Software Architecture
Computer security
Networking