When we put out an ad for a game programmer we get many hundred responses. Sometimes several thousand responses.
The first pass is just to prune the huge pile down to something we can print without feeling guilty about killing a forest.
If you aren't in the same geographic area or you don't have a university education or you don't have some game development experience or you don't have some other immediately obvious thing that says you must be hired, your application will not survive the initial cut.
If you are qualified to do the work but you don't have the traditional credentials for the job, you will not be interviewed for the job.
It isn't that we don't think you can do the job. You probably could do the job just fine.
The problem is that you are not in a vacuum.
If you don't have the education and you don't have the work experience, you need to find an alternate route into the industry.
The simplest alternate route is networking. You need someone inside the industry to take note of you, and you need that person to convince their company to hire you.
Most job vacancies are filled by networking. Somebody you know recommends you for the job long before the job is ever advertised to the public.