Well at the very least it presents a soft target for hacking into his personal email adddress (it's gmail not govenrment) and secondly, compromising it literally gives you access to dial into cabinet meetings.
Read my edit. Email addresses can be received through public records requests routinely. It's a public record!
Posting something like that on Twitter is like a dare.
This email address could be at any provider - perhaps it's his personal gmail address, for example.
And like one of the other comments in this chain points out - his personal email address was being used for government affairs, and that made it open to public records law suits. The public already has access to it.