I bet most people answering this question do so not by any sort of reasoned consideration of how important work, family, sleep, video games, music-making, sport, etc., etc., etc., are to them, but by a quick System-1-ish consideration of how the question makes them feel. And I bet anyone using this question to measure "conformity with masculinity" or any other psychological characteristic are relying on that. This sort of thing is omnipresent in psychological questionnaires, which I guess is what you're getting at in your second paragraph.

So, anyway, the sort of things I would think about if I were trying to answer this question while taking it more seriously than I think its authors did:

• What would hurt most to lose? (This is Tem42's approach.) By this criterion, work comes out quite important but other things -- e.g., my family -- clearly ahead.
  • But that may be misleading; e.g., one reason why losing my job would hurt less than losing my daughter is that I can probably get another job much more easily and quickly than another daughter. But that doesn't seem like it's the same thing as importance.
• What gives me most satisfaction? By this criterion, work does OK -- I like my job pretty well -- but many other things do better.
  • That may also be misleading. If I really disliked my job but had no savings and a family to feed, work might be very high up on the list of important things while still coming below Nothing At All in satisfaction conferred.
• What do I spend most time thinking about?
  • Could well be work. But does this mean that if my employer suddenly demanded double the working hours (and for some reason I couldn't refuse or quit or anything) it would become much more important to me? I'm not sure that's right.
• What do I voluntarily put most effort into?
  • Could well be work. But it seems like we should be distinguishing intrinsic and extrinsic motivation -- a major reason for putting effort into work is simply that I get paid for my job and I like being paid, and that's not obviously the same thing as importance.
• What do I think most valuable to the world?
  • I think this is a very reasonable sense of "importance" but probably too far removed from the questioner's intent.

If I were fired, this would be bad, but not too terrible. If a family member died this would be worse. I could come up with further examples, but there is no need to; I now have enough information to answer this question: don't agree.