There's no possible way they could have a secure electronic ballot . It's not possible to both transmit the ballot securely while at the same time ensuring that the conflicting objectives of vote secrecy and vote uniqueness. In order to ensure uniqueness (so the same person can't vote multiple times), there has to be a unique id (such as a token, username&password, or even voter id number, ssn, etc.) that is linked to a single human being. But, in order to to have a secret ballot, there has to be no way to link a specific person with the vote that was cast. With in person voting, or even mail-in voting, the two things are separate (using a separate inside envelope containing the ballot, and an outside envelope containing the voter id in the case of mail-in voting). With online voting over the Internet (and I'm counting the satellite link to the ISS as part of the internet for this discussion), they must necessarily be both provided in the same session.
In the article, it mentions that there's a secure link from the ISS to the computer on the ground. But what happens then? Is the ballot printed out and mailed in? If so, ground crew have the potential to see the ballot. Or, is it transmitted electronically, in which case, the above point about transmitting both the unique id and the vote.
Why didn't the astronauts just file an absentee ballot before leaving?