I'll probably be more upset the day The NY Times stops publishing the print edition.
DMOZ is without a doubt an icon that has jump-started web classification with hundreds, if not thousands of entrepreneurs rushing to run their own Yahoo!, whether based on DMOZ api or their own. It has served the web well. In terms of SEO impact, I don't think there will be a meaningful effect, since the game has changed so much that a tweet is probably of more value to your business than a listing at this classic catalog.
In a metaphorical way, DMOZ is the newspaper of today's news media.