Since this is for university...

From my own experience with university mandated internships, my advice is that once you have found a place to do the internship, to go to whoever is responsible for approving it at your university and have them confirm that this is a valid place. I did my engineering internship at the NRC in Canada and afterwards my university said "We would not accept this, if you hadn't checked with us beforehand", even though it was 100% according to their guidelines...

As for the companies, you already made up your mind to go with game studios, so go for it! Here's Wikipedia's list of video game developers.