Re: non-citizens, no, for even better reasons. If one country's policy actions are hurting the citizens of another country, the proper forum isn't a lawsuit, but rather the battlefield.
Hold your horses there, fella. It's 2013, we invented this thing called WTO, and this other thing called UN... I think we could give them a whirl before we start going von Clausewitz on everyone's ass.
As for the WTO, international surveillance is not a trade issue, it's a security issue. It's totally outside the domain of the WTO. One country's maneuverings for its security interests impinging the citizens of another country is the classic use-case for war.
The inanity you're referring to is this: surveillance of the communications of any individual American would reveal that all Americans are under regular surveillance. It's not really as inane as you think, however that doesn't make it any less ridiculous.
This was in the news last week itself: http://news.oneindia.in/international/us-federal-court-summo...
At the very least, shareholders of companies like Yahoo! are seeing lower shareholder value. That's a loss. They're harmed. There's a lot greater harm than that, but at least it's a starting point.
EDIT: come to think of it, I don't know why I wrote citizen of the country. Citizens aren't the only ones hurt. I'm no lawyer. Can non-citizens sue too?