False. The Airport Express is definitely a router.
While I somewhat agree, the airport express is more of a solution to generate wi-fi so that you can have multiple devices connect to the internet, or network wireless products, ie. printers, apple tv, etc... But the good thing is that the airport doesn't have to directly plug into the internet gateway box.
From apple:
Introducing the new AirPort Express Base Station, now with 802.11n wireless. Easily create a wireless network at home. Enjoy your iTunes music library in virtually any room of your house. Share a USB printer without obtrusive cables. And do it all with the latest wireless technology.
And as in the op for portability:
Take it with you
Lightweight and compact, AirPort Express is built for mobility, so you can create an instant wireless network at your hotel, job site, or wherever you need one.
I can't remember if the airport utility had a method of entering the isp information in order to connect to the internet and become a router via the gateway. Usually a regular router you do buy, requires you to configure the type of connection with login information to access your internet. It generates multiple ip addresses to allow for other computers to connect. So in a sense, the airport is like a router allowing multiple devices to connect with an ip wirelessly.
If you mean the term "router" in the broader sense as it does generate multiple ip's for your devices like a router, then I agree. Sorry for the reply.