It's a relative clause, which normally follows the thing it describes, but in this case you have two things (fake accounts and rumour-mongering) given as examples of the "issues".
The sentence is a bit sloppily-punctuated. It should read, "The real-name rule also addresses issues, such as fake accounts and real rumor-mongering, that Chinese users don't actually object to." Frank's rephrasing is perfectly clear.
PS. "mongering" doesn't exist as a word by itself. It's "rumour-mongering" which is the noun.