I'm not quite sure how any of those supply side effects could cause unemployment or wage changes on the scale of what is happening in Greece. But if you could explain how those effects could have led to the unemployment and wage drops we've seen in Greece I would love to learn.
It seems to me there are two possibilities.
1. When Varoufakis talks about macroeconomic models taught at the best universities feature no accumulated debt, no involuntary unemployment and, indeed, no money (with relative prices reflecting a form of barter) he is talking about Keynesian.
Keynesian theory includes involuntary unemployment, accumulated debt, and money. So Varoufakis would have to have been mistaken. And he is shown to be especially confused when he later remarks
Moving to the micro level, the observation that, in the case of Greece, real wages fell by 40% but employment dropped precipitously, while exports remained flat, illustrates in Technicolor how useless a microeconomics approach bereft of macro foundations truly is.
This means he believes Keynesians are especially focused on microfoundations and ignore macro foundations. When this is actually true of the Neoclassical school. Then there is the issue you brought up. Varoufakis critiques Keynesians at the beginning and then appeals to it at the end. This implies he does not understand the basics of Keynesian theory. This is very surprising because he thinks of Keynes as one of the economists that personally influenced him the most.
2. Varoufakis is actually talking about Neoclassical economics.
This makes a lot of sense. Many Neoclassical economic models lack money, don't have involuntary unemployment, and lack accumulated debt. In addition it is very hard to tell a story about large wage drops, and growth in unemployment from microfoundations(basically supply-side). This means he is being consistent when he later appeals to Keynesian economics.
Varoufakis is obviously a very intelligent man who has spent 28 years studying economics. I would be incredibly surprised if he was confused about the basics of the two most influential schools of thought in macroeconomics.