Should a job seeker be more concerned with the responsibilities or the
qualifications? How should these sections be interpreted?
Why attempt to choose one or the other? Both are valid clues as to the nature of the job, and thus both should be considered by the job seeker.
The responsibilities should talk more about the job itself. The qualifications should talk more about the candidate.
Yet both together provide a picture of how the company envisions filling a particular role. As such they should be read and understood by the candidate, and referenced during interviews.
It can be powerful to tell an interviewer something like "I see you are looking for a candidate with experience in X, Y, and Z. Let me tell you how I've used those technologies successfully in my career so far." Then follow up with specifics.
It's also powerful to say something like "I see the person who lands this role will be doing A, B, and C. Let me tell you about how I've done all of those many times." Then follow up with specifics.
For both qualifications and responsibilities, it isn't necessary (or even desirable) to touch on the pieces that you lack. If it comes up, you can reassure the interviewer that you already know so much (many technologies, for example), that learning a new one won't be difficult. You can even talk about how you have learned new technologies in the past, for example.