Most people "google", not "dmoz". The only real use is from the search engines and SEO's. Search Engines use it because of the human approval of websites listed, so they include it in their algorithm so they don't have to pay humans themselves to do it and haven't gotten their algorithms good enough to do it automatically. And SEO's only try to get their sites in it because they know it's used by the SE's in their algo's (plus it's a link). The normal average surfer doesn't use it, and a lot don't even know what it is.
If the search engines didn't use it in their algo's then no one would care other than the editors themselves? Why are the editors doing this valuable service for the SE's for free. I can understand and do understand the need for DMOZ 10 years ago. But, in today's web environment, all I see are the editors doing free outsourcing work for the SE's.