Interesting, thank you.
"Whoever embezzles, steals, purloins, or knowingly converts to his use or the use of another, or without authority, sells, conveys or disposes of any record, voucher, money, or thing of value of the United States or of any department or agency thereof, or any property made or being made under contract for the United States or any department or agency thereof; ..."
It's definitely possible to imagine a situation in which Snowden "knowingly ... sells ... any record ... or thing of value of the United States" to Russia, namely a copy of the information he had available to him while working for the NSA.
I'm not sure how courts have interpreted "record ... or thing", and whether (for example) a copy of a page from an internal government wiki would count, but let's assume that digital information is a "thing" and that copies of it are still "of the United States".
I'll further grant, for the sake of argument, that the US government has secret evidence that such a selling did take place (perhaps witnessed by a double agent working at the Kremlin, who could be called upon to give a witness statement at a trial held in secret), although I don't actually believe such selling occurred.
My main point, though, was that I don't know of any court interpreting "steals" in a statute to mean "making an unauthorized copy of" or "leaking". You're right, though, that there are other laws that cover what Snowden did.