There must be thousands of jobs that want just that.

Agreed. But that's still better than many.

>but even as a designer she has failed to demonstrate good design sense

Can somebody explain what's wrong with this design?

tptacek did an excellent job of explaining it for you already. It sounds a bit like you are thinking of design as "making things pretty", and it's not. It's about communication.

The message this resume is communicating is that the author also feels that design is just about ornamentation, and the only way it could be more obvious is if the diagram were in the shape of a giant duck. I have to assume she doesn't actually believe that, not least since she hasn't asked for us to psychoanalyse her and it's really, really unfair to try to do so based on this completely decontextualised link. But even so, the design seems unsuccessful to me because it's communicating the wrong message.

Design is about communication, but it does not exclude ornamentation. Design can be ornamental (if the purpose of the resume is to highlight some design skill), however it should not reduce the readability of data as this one does. Having just read "The visual display of quantitative information" I have this to say to the designer of the resume: remove non-data ink. Increase data density and readability. Especially readability.

It's flashy and harder to understand than more boring presentations?

I understand why it might not be a great resume, but what about the design. The Previous Work tree diagram is sort of neat, in text form the info that it conveys might be even harder to understand.

It's a bad design because it does a bad job framing the contents. It doesn't solve a problem, instead it creates several. It took me several times longer to figure out her resume than it does for a standard one, not to mention that I still came away not knowing several things that I would need to know.

As it stands, all I can say about her is that she has decent mastery of Photoshop but no understanding of good design.