What does "piracy pirates" mean?

Solution 1:

It's a (rather unfunny, IMHO) variation of the (rather unfunny, IMHO) "In Soviet Russia" meme. The most famous examples are probably "In Soviet Russia, TV watches you!" and "In Soviet Russia, radio listens to you!"

Encyclopedia Dramatica has more examples.

So, what the sentence basically says is, "in all normal countries, you pirate stuff, but Soviet Russia was so backwards that stuff would pirate you".

Solution 2:

It's a style of humour originated by Yakov Smirnoff

http://en.wikipedia.org/wiki/Yakov_Smirnoff#Russian_reversal

For example

In America, you assassinate president.

In Soviet Russia, president assassinate you.