Well, it's running for me, but I couldn't join any games.
Half were full, and the other half just dropped me back to the browser with no error.
After enabling the console, I could see it had been erroring out with "This server requires that Steam be running" or somesuch, when (as it happens) Steam is running, because that's how I started HL2:DM in the first place. Firewall issues, maybe? Hrm. I wonder.
Took Steam forever to start the first time, though.
Probably for the best, anyway. The first release of any MP is always a laggy stack of JoeBob's running a 32-person server on their Celeron and DSL.