Yes, the Yun can act as a full blown router, but that is not the default configuration. By default:
- WiFi is a hotspot, and serves DHCP addresses to WiFi clients that are associated with its hotspot
- Ethernet is a client configured to get an address from a DHCP server
When you set up the Yun's WiFi to be a client to connect to a WiFi network, it no longer serves DHCP addresses over the WiFi link.
I'm sure that you can set up the Yun to be a DHCP server, but I don't know the procedure. You may be able to get some ideas from the OpenWRT web site, or from someone with more Linux experience than I.