I've got to be honest and say I don't know. The fact sheets they've got out there is all i'm working off.
In my personal experience, since they don't define it, that means it is either:
a commonly used term in workplace law already defined elsewhere
based off of the ordinary dictionary meaning of the word
loosely defined and therefore subject to discretion without limiting the authority to specifics.
I had a quick look around and the fair work commission has a definition, and that's probably where the buck stops:
(My emphasis)
There are several other legal or .gov.au authorities on the definition and they all seem to be fairly similar.
My personal opinion on it is that the line i've bolded above is the crux of it. Regular doesn't mean frequent or often, just a recurring pattern, so "on the books for a year" would broadly tick the box, provided shifts were offered periodically suiting the worker's availability (which could even extend to "only during school holidays" if the employer found that arrangement workable), and that worker accepted the offered shifts regularly enough (which doesn't mean they had to accept every shift either).
If you were still "engaged" (or, "on the books") as a casual simply on the basis that you hadn't resigned and they hadn't terminated you, but you weren't offered or considered for shifts, and you never asked or made yourself available to be rostered, then you arguably aren't employed on a 'regular basis' as there is no recurring pattern of availability or shifts offered.
Thats what it seems like, in my opinion anyway.