Why is EAX not a generic composition?
When reading the paper, it seems that there are three or so properties that make a generic authenticated encryption method:


a generic encryption method and MAC are used;
two different keys are used for both;
two pass encryption is used (generally encrypt-than-MAC).


EAX uses two well defined algorithms: AES and CMAC. So it seems the definition fails on (1). As EAX uses only 1 key it will always fail on (2) as well.

But yes, if you do not consider the special way $\mathcal{N}$ is constructed then EAX outputting just $\mathcal{C}$ could be considered a relatively generic construction when it comes to (3).

Adding it up, I personally think this should be a big NO, EAX is not a generic construction as defined in the paper; and just outputting $\mathcal{C}$ only makes a tiny difference.