Game Company Internships for High School Students?

Although I cannot speak for game company specifically, in general in regards to internships, a couple of factors comes into play. Don't expect to get an internship with the expectation they'll just teach you everything you need to know. Try to do some side projects and demonstrate that you have a basic understanding of the skills you need to do well on the job. If you look at job postings, many may put things you must have and nice to have. Work on having a portfolio that demonstrates you have those kind of skills.

Networking and people skills are just as important. Go to networking events and talk to recruiters and hear about companies and find out what you specifically are looking for. Although at first many of them would prefer some college education, it is not needed if you can show you have the traits they may be looking for. Attitude is much more important as companies want people that fits well culturally with the teams and overall easier to work with. Persistence is also important; you have to keep trying and don't get deterred if you don't get it the first couple of times.

As for more practical steps, if you are looking to do a side project, I would check out Google Summer of code. Although it's closed right now, you can try applying for one next year. Another good place is to take some coursera courses and work on and improve on the assignments on some courses which could be used in your portfolio. Best of luck!

As someone else mentioned I think you need to be looking for a smaller studio for this type of internship. I can say that the studio I work for has hired HS students in the past for summer interns, we spoke at the HS a few times about the game industry and then gave out paid internships. Make sure you work on MODS (there are MOD teams that you can join and work on a project) and learn programs like Unity3d or Unreal if you are trying to be a designer. If you are want to be an artist work in Maya or Blender (FREE). If programming is your dream buy some books and get coding. For any of the above watch as many YouTube videos and tutorials as you can and just work on projects.

The more you work on and learn the more valuable you are to a studio.

I'll just echo the other replies. Internships are like golden unicorns -- they're pretty rare. Think about it from the studio's side: You want to take time away from one of the team members, who totally knows his job, to spend time helping someone who doesn't know what they are doing. There just isn't enough slack in the development process to do that. You might be able to shadow someone for a day, but they can't give you things to do. There's too much risk.

A different option would be to find an indie developer who's not in a time crunch and would be happy to hand off basic repetitive tasks so they can concentrate on the hard stuff. Check your area for Meetup groups focused on game development or Unity users. That might work. Also get in touch with the closest IGDA chapter you can find. IGDA.org.

If you want to get an internship, you should have something to show or demonstrate that a) you are serious, and b) that you are useful.

In other words, if you want to be a designer, have some maps or a mod as a portfolio. Want to be an artist? Have some character models, maps, concept art, etc. Engineer? Write some code that does something.

They may still take a college intern over a high school student because of liability (e.g. you may need to be 18.)