You use the "update listing" link in that category to request any kind of change, from misspelled word in description to category change, listing removal, or, as in this case, URL change.
Include a brief explanation as to why -- "it's my site, and I'm moving it to a different domain" is plenty.
And if at all possible, make sure that when a surfer (whether ODP editor or not) goes to the OLD domain, he comes away with the impression, "this site has moved to a new domain."
Why do this? Remember that you cannot "request" a change at all, you can only "suggest" a change (it's a whole different attitude and mindset.) We're happy to get anybody's suggestion -- and if you are the real site owner, we really WANT to know what YOU know about what the real domain name is. But we aren't going to take ANY suggestions until we check them on the ground -- and in this case, the relevant ground is the OLD domain. An editor might well say, "hmm, this domain doesn't look like it's moved. dunno where this person gets off claiming to be the site owner, when anyone can see the site is still alive and well at its old address." (And that is not what you want to happen. So, if you can, make sure it doesn't happen.)