Many interviews will ask you to speak about a game you have played and talk about the good and bad, often requiring you to go into detail. There may also be theoretical challenges to expand or limit game mechanics, so it definitely helps to be familiar with that (or to only bring up games you feel confident dissecting
).
Ultimately I think actual content will speak much louder than any sort of game analysis document to show you know your stuff. That said, studios often have a few people that will share their experiences with games or film or whatever and are able to pick out great bits of information that can prove to be pretty useful. It might be useful to try an exercise like this but I don't think I would have it as a primary feature on a portfolio.