There's a few avenues: 1) Publishing classified information. Easy to show that he did this but a very difficult path to go down when American newspapers do this all the time.
2) Conspiracy to commit espionage. Probably the most likely, this would require showing that he was actively working with someone to extract classified information. Just openly soliciting leaks to an email address wouldn't be enough, he'd really have to be talking to a leaker before/during the extraction of the data. Depending on the nature of his communications with Guccifer (The GRU hackers from 2016) they may be able to make a case on this basis.
3) Al Capone style / collateral attack. The US made it very hard for Wikileaks to operate financially. Maybe he did something that falls under the US' capacious money laundering rules?
Note that this case is fundamentally different from Manning / Snowden / Winner who all had access to classified information legally and misused that access. Due to the first amendment, American espionage laws are quite narrowly written compared to those of many other countries and while it is easy to prosecute people on the "inside" for leaking classified material to the "outside", it is much harder to prosecute someone for what they do with it when it's out.
(Edit: Well that was fast! Interested to see what's in the indictment)