OK, I figured it out. Even though I'm using 2.2.1, I needed to download the 2.2.2 beta and to use the exact directory structure so that the templates and cairngorm.xml file can be found.
I think the setup directions could clarify a little more, "Plugin with the Cairngorm 2.2.1 SWC, which can be downloaded from here, it only requires the 2.2.2Codegen-beta distribution for the codegen templates that are packaged with Cairngorm."
It wasn't super clear that 1) I had to maintain directory structure 2) that setting up the Cairngorm plugin in Eclipse was looking for cairngorm.xml file 3) that I should unzip the 2.2.2beta version, then copy my old 2.2.1 swc over the new one.
Thanks.