I'm not an expert on relevant US legislative acts, but this is the legal definition in local laws here and I expect that the term of espionage have been defined a few centuries ago and would be mostly matching throughout the world.

A quick look at current US laws (http://www.law.cornell.edu/uscode/18/usc_sec_18_00000793----000-.html) does indicate that there is a penalty for such actions with 'intent or reason to believe ... for the injury of United States or advantage of any foreign nation' - so simply acting to intentionally harm US would be punishable as well, but it's not calling it espionage. And the Manning issue would depend on his intention/reason to believe about harming US vs. helping US nation, which may be clarified by evidence in his earlier communications with Adrian Lamo and others.