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.

The real-name rule also addresses issues that Chinese users don't actually object to, these issues are such as fake accounts and real rumor mongering.

This is a complex sentence. The word "mongering" is a noun, so it cannot have an object. To which clause do you refer? "Chinese users don't actually object to" is a clause that modifies "issues".