A news site called Greek Reporter ran an April Fool's joke suggesting Varoufakis would move the country to use the cryptocurrency, but this is definitely real.
The video is called Bitcoin and the Digital Economy and it's by Kostas Mouratidis, a journalism student in Thessaloniki.
The documentary titles him as finance minister of Greece and it seems like it was filmed recently - but if it was done before late January then he wouldn't have been in office yet, but it was only uploaded on April 9.
Here he is (from 0:45) - there's a transcript of Varoufakis' comments below if you don't want to watch the whole thing:
"There is no need to pay commission, there is no need to pay debt to any banker."
And then he's back in around 3:45:
"Bitcoin's organisation became so that those who use it participate in a community where jointly they follow every Bitcoin's move. In other words, it's like all of us who participate in Bitcoin to be members of the central bank of Bitcoin."
And 4:27
"There is an absolute democracy and those who are in fear of manipulation of money by the banks or the bankers feel involved in a monetary system which is released from these dangers."
And from about 9:18 again, he's talking about the flaws with money as it exists right now:
"Each tool can be used for good and evil purposes. Let us not forget that in Europe the European Central Bank produces the €500 euro banknotes. I do not think that you and I have used them very often. They are the notes that drug dealers especially love.
What does this mean? Does it mean that the European Central Bank created these notes for drug dealers? The solution of these specific problems needs to be found elsewhere."
Then he's back again after 10:30, being more critical about the cryptocurrency
It will never be able to replace the currencies that are controlled by a central bank. At least it will not be able to do it in a way that can be sustained...
How will the state control these transactions and how will it tax? So it creates major problems on the issue of taxation. To perform under the fantasy that each of us can function as a Robinson Crusoe in our own isolated island, and all together to be in this archipelago consisted of a Polynesia with small islands where everyone is the boss. I think that's a fantasy which ultimately leads to economic crises like the one we have right now.
There's a reasonable question to ask about whether this is the best use of Varoufakis' time, but he's written blogs about Bitcoin a number of times, so it's clearly a pre-existing interest. And to be fair, it's very cool of him to have given an interview to a student for their work.