However, so far I have been rejected from every single internship I have applied for, all of which are offered by game engine companies such as Unity and Epic Games.
Do you know who is rejecting you? As in, are you even getting passed HR? Unless HR/recruiters really understands what the team is looking for, often if you don't check enough boxes, you will be rejected. It could be something as simple as not having graduated yet, to not having any/enough work experience.
when I went to my first GDC last week, I noticed a few things. AFAICT it seems the difficulty in getting an offer from game companies stems from an absurdly high volume of applicants, and many of them are young programmers willing to get paid below-market-rate salaries. One of the members from this community went to give out a resume to Insomniac Games at GDC, and they were so saturated with applications they didn't want to look at his at all. The rejection had nothing to do with his experience or credentials ... Given your Monter side project, you're already ahead of many graduating programmers, and could probably get a decent job offer anywhere outside of games fairly quickly.
A budding game developer and programmer
Hopefully something comes up :). A couple things I would say is that I agree with Abner of possibly working in a related field with less competition to gain experience then moving across into game development. Having a look at your resume, I feel like you could expand on some things you've done. You've got a link to the Monter blog, but maybe try convey more in the resume. I agree with Brian that you got to sell yourself (in a good way). Take the tips with a grain of salt, (I haven't got a job in the game industry) but here's what I would do:
1. Have expanded sections for each project and have accompanying screenshot/image. Monter looks super nice/beautiful, make sure you get that across. Have a bigger writeup of what the projects involved, what you've had to learn.
2. Expand on education/university section. What subjects/projects you did as part of the university course? Even if you feel like the subjects weren't anything special, what would a employer like to here. Are there any clubs you were in at the university? Any team projects you worked on. I think even if its web related, still shows you've worked in a team etc.
3. Have a cover letter. Expand on the personal reasons why you would like to work in the game industry.
4. Make the resume bring across that "you would be mad not to hire me!"
5. Extra: Put the resume on a website so it's easier to navigate?
Here is a resume/cover-letter of mine: (not the best example, but maybe give you some ideas).
I think the best bet is keep trying. Maybe find a way to get passed HR department?
So think of these (one-page resume) rules as merely guidelines. To one person looking at a stack of resumes, their criteria might be to only look at one-page resumes. For others? One page is the first to throw out (for they might assume this person does not have enough experience). Some might need a few years work experience; while others, might require a bachelor/master/PhD. It's just the nature of things unfortunately.
I know for recent graduates they say one-page resumes for what tends to happen is people will pad it with stuff. Padding is not good. It is obvious most of the time when someone pads their resume then you start to wonder why?
But, if you have experience, if you have things you can share, be concise; but, you can list things that will push you greater than a page.
Looking quickly at your resume, you need to understand that you are using very specific terms to refer to things that you've done or are working on. Nothing wrong with that, but try to think if someone who was not familiar with the tech side of games (such as a bad, or perhaps just not as informed HR person), what would they understand?
I like your personal projects section. But the rest of your resume seems empty. Though in your case, I don't think adding more to it would help, unless you have work experience, or projects done in school worth talking about. Or you've done volunteer work. But what would help would be a cover letter, which you would need to tailor it to the job that you are applying to.
Though unfortunate, what Abner said is true; but, it's also not a new thing. When you have 200 resumes on your desk, it can be hard to stand out.
P.P.S. I realize the irony that I left NASA and now work for the games industry. In my defense, I'm working on compilers, not a game :P
A C++ Programmer working on Squad professionally, and Proportion during my free time.
Web Developer by day, game hobbyist by night.
You are applying for perhaps the hardest to get programming internships in the whole world.