They mentioned in the video that border control at the airport will make sure nobody can leave Cyprus with more than 3000 euros per person per trip. I happen to know of a way to get more money of the island, faster and cheaper. Perhaps someone should tell them.

They (authorities) don't care. You may buy bitcoin in Cyprus and transfer it abroad, but EURO still remains inside the country.
Actually, EUR in cyprus in not the same EUR as in the rest of Europe as you cannot use it abroad. It's like different currency which cannot be converted into other currencies. I suppose that EURO inside Cyprus may cost only 70% of EUR abroad.