Just found this thread when looking to find out who clients are myself, didn't notice "Wireless Clients" was click-able either, that's bad interface design from Apple!
Anyway, the DHCP tab will be greyed out or useless (empty) if you are using your airport base-station in bridge mode, most likely if your airport express is connected to an ethernet router for example. This is what my set-up is basically.
But that doesn't help in finding out IP address and/or machine-name. Is there another way this information could be obtained? As I have some "clients" showing up on my airport express that aren't showing up in my router (i.e they're connected to the base-station but haven't been given an IP by my router). I suspect it's simply another wireless computer connecting to the wrong base-station (I have two for better signal strength on different floors of my house) and my XBox 360 which is plugged into the ethernet port (but switched off), but it'd be nice to check remotely rather than having to copy each machine's MAC address!