I'll bite: If he signed this, it's pretty much open and shut that he has to forfeit all proceeds from any sales of a book or other medium containing said secrets. However, if the medium does not actually contain any secrets, but is rather about his ordeal and experiences as a whistleblower, well that's not covered by this document. Hence why the state is suing instead.
Otherwise, I doubt that Russia will care any more about this than they've cared about extradition demands. But even if his book was published in Russia, global distribution would be difficult. While I'd actually prefer to pay with Bitcoin via Tor, that wouldn't work generally.
On May 20, 2013, Snowden flew to Hong Kong after leaving his job at an NSA facility in Hawaii...
Perhaps this older revision[2] may be more relevant for the time; wasn't successful in discovering a complete revision history of the form.
Leaving it to the lawyer types to diff and discuss.
[1] https://en.wikipedia.org/wiki/Edward_Snowden
[2] https://www.secnav.navy.mil/dusnp/Forms/sf312.pdf
EDIT: As it were, item 5 is still there.