It's worth noting that this article is not about e-voting in the sense that the video seems to be presenting . This is about the machines that tabulate the results, often from paper ballots manually filled in by voters.
The report itself  goes into more detail on the exact nature of the vulnerabilities.
 I admit I didn't watch the whole video; I find video to be an extremely tedious medium for transmitting information like this, but from skimming bits of it it seems that the speaker is more focused on distributed systems for voting and online voting systems, which are both horrifying ideas; although Oregon and Washington have made a good go at absentee-only voting.
Apparently there is a report from Defcon that describes in more detail what the vulnerabilities are . I have not yet had a chance to make a more detailed review.