How to critically review an article when one doesn't have proper background knowledge?
This is really the whole point of the challenge the supervisor has presented you. I bet he was hoping to hit you with something that wouldn't exactly be easy for you. He's trying to get you to stretch a bit and get out of your comfort zone. I don't know what he intends by the review format that he gave you, but if you have any critiques, concerns, or other thoughts about this article, this is where you should put them. It almost doesn't even matter if you're right (almost), but you need to show him that you've thought about the article, that you can explain its implications, and that if there are things that worry you about it, that you can explain them. 

If you are really stuck, it's probably worth looking through some of the articles that are cited by the article in question to give yourself some more background. This should also help you set the article in the context of some of the rest of the literature.