no, he is using it incorrectly. A WAN router would be a router that operates across a WAN, and manages connections in the WAN. If anything a home router is a LAN router, because it manages a LAN. Technically you don't need a WAN port on a router, you could make it work with just custom settings on the router and on each device on the network and use the router as a switch.
But it makes it much much easier to setup with a WAN port. The WAN port will have its own IP address, which is very useful because that can be assigned a dynamic IP from your ISP's DHCP server. Then you can have an internal LAN IP address for the router to access the GUI somewhat securely(even without https/etc). A home router with 2 WAN ports would probably have a setting to automatically route internet traffic to the other WAN network it is connected to if one of the fails. Or it may allow you to router certain types of traffic, or traffic from certain machines on the LAN, through a particular WAN port. Would depend on how the manufacture designed the routers firmware.
WAN routers would be the big super expensive ciscos/etc ISP's use I would say. Though I don't think that is the technical term...but those operate on a WAN and manage part of the WAN.
Whatever the router manages would be what it is. If it manages the WAN, then WAN router. if it manages the LAN, lan router, etc etc. Your' ISP would kick you off the network if you start trying to route WAN traffic on what is their network.