Uh. DCC (Direct Client Connection) has next to NOTHING to do with IRC with the sole exception of the CTCP that starts it off (not the notice).
Basically what happens is the initiater (person who will do the listening) sends a CTCP (PRIVMSG starting and ending with ASCII 1) DCC. The "reply" to this request does not occur on the IRC connection. The DCC ctcp includes the IP in long-integer form (see mIRC's $longip for what I mean) and a port number. To accept the connection simply connect to the specified IP and port. To reject the connection, simply do nothing.
The -nick- DCC Chat (IP) that appears is just something extra mIRC (and possibly other clients) send but from what I understand of DCC it is not required to establish a DCC session - the information required is in the DCC CTCP.