DHCP servers assign dynamic ip addresses. yahoo's chat server does not act as a DHCP server.Everyone that connects to yahoo chat has their own ip address before they get there. This can be assigned in different ways, which is another topic altogether.

All chatting trasactions are done on the chat server and you can only get the ip address of machines you have established a connection with. the only address you can get while chatting is the chat-servers because thats the only machine your connected to. If you want to find someones ip address you must establish a connection with them.