I would have said anything you do behind your partner's back, which involves intimacy of any kind, whether it's face to face, writing to them, texting or telephone conversations can be construed as cheating.
Even if Bubbles's partner has never met this other person in the UK, the fact he is corresponding with her would to me, mean there is some kind of intent there. If the E mails are intimate in a sexual or romantic way, then he obviously is not happy in the relationship and is clearly seeking something else.
I expect few women would need to ask, "how does someone cheat by e mail"!!