In addition to yadokari's great answer and for lack of space in his comments I'll write up what ive found here.
Amongst other uses of という one is often used to attach a modifier to a noun clause.
From the given example
「ＮＳＡは中国に対するハッキングをやっていた」is the modifer
暴露 を行なって the noun clause.
It's often used especially when the modifer is either
- a question
- or simply very long
Heresay i.e. information received from other people that cannot be adequately substantiated or a rumor.
It would indeed make sence to use という here to connect the noun clause 暴露をおかなう with its preceeding modifier. After all the reporter can only allege that the NSA is hacking China (at the time anyway, its been verified as true i now believe) so its heresay.
This I believe is what people mean by air-quoting.
Now onto the last sentence in the example
I believe this is just because the writer felt the modifier Ｇ８会議が北アイルランドで始まる was long and felt the need to join it to タイミング with という。Just to help it read better.
This is why という isn't always translatable into English - its merely serving to make things flow. Just as Yadokari said, if you were to translate it, the most suitable direct translations like "to say/called thusly/meaning/in other words/so to say." would result in stuffy english.
As for using という to connect a question modifier with a noun clause I'll demonstrate with this example
there was a conversation of how to strengthen the economy.
どうやって経済を強化するか modifier (question form)
Thanks again to yakokari's answer.