OK, you've learned something. You can add another name to your personal list of gormless gurus: either me or your e-text author (I don't care which).
DMOZ (the cognosceti generally call it the ODP, for "Open Directory Project") isn't a search engine. It never was a search engine, and it is highly unlikely that it ever will be a search engine. It is, as its name suggests, a directory. (The site indeed possesses a site search, which is a hack of a free-software search tool that possesses no concept of rank, relevance, stemming, any kind of semantic tools, boolean search phrases, or ... anything that you'd normally look for in a search engine. It helps us place sites, and if it does something else good for someone, we won't begrudge it.)
Some real search engines pick stuff up from the ODP. Google does a pretty good job; some others don't do so well. We don't mind: we tend to think human-edited link lists are an important contribution to search engine quality, but the Search engineers are entitled to their own opinion.
There are two little bits about the ODP that your guru should have mentioned.
One is: The ODP doesn't list all sites. It is selective; many sites that most desperately need promotion aren't listed at all.
Another is that the editors are volunteers who work on what they consider most important: which is seldom what commercial webmasters want. A site may wait an indefinite period of time for a review; and the webmaster really has no estimate of, or control over, how long that will be.
So depending on the ODP as a site promotion strategy is asking for failure: at the very best, it will do nothing for you that it wouldn't happily do for all your competitors!
But, considering the expense of an ODP submittal (a few minutes to find the best category, and another few minutes to submit the site), it is probably about the first thing you should do for a site you want to promote.
And then...(this is the important bit) forget it! Go on about your promotional schemes or ruses as best you can. Assume that the ODP will never list your site so long as you need a listing. But the moment your site is established and has no more need of promotion, some editor is liable to think, "The ODP can not for a moment longer be considered comprehensive without listing this very site" -- and list it.
So: how important is it? Important enough to submit to. Not important to depend on for commercial promotion. Not important enough to worry about.
Practically speaking, I think that's about all that matters.