It is more than that.

* You need to apply at the right time. The application window for being a summer intern is very short.
* There will be few openings. A studio might have one or two jobs. Contrast with when a studio needs to hire a full team. There are still a lot of unemployed game developers, so why hire an intern when you can get a regular full-time employee?
* You need to be the best. There will be a tall stack of applications, they will eventually eliminate nearly every one.

You can directly control applying at the right time. You do that by asking the studios when they are hiring interns.

You can indirectly control your perceived quality by building a portfolio of completed games or game-like projects, participating in industry groups like SIGDA, and making contacts to get a direct referral rather than traditional application. Nothing on there screams the message, "I am passionate about making games."

The other very important fact is your graduation date. You're at least a full year out from graduation. Put in the month you plan to graduate in addition to the year. Again, remember that there are likely interns who are recent graduates or who finish up this summer. That puts you at a disadvantage.