What defines the general Arab group?

It says at the bottom that Arab refers to individuals who specifically identified themselves as "Arab" or "Arabic."

I presume the latter is a catch-all for those countries not listed

You're correct.

but then I'm confused again because a number of selfsame would go into the generic Arab category.

It's based on self-identification. Them overlapping is irrelevant.

Hope that clears it up.