One commenter above called out the elephant in the room: you're categorically a career hopper, not a job hopper, and that is indeed worse in the hiring manager's eyes. If they suspect you'll be leaving the company in six months, either voluntarily or they'll have to send you packing because you can't keep up, they won't want to hire you. The jumping between careers shows a lack of commitment, planning, and decisiveness. This is not to be offensive, but rather to be blunt and helpful.
While I work more with industrial systems and real time operating systems (RTOS), game development is not easy by comparison. One has tight deadlines, often works massive overtime, and at least in the US and Canada, one usually works in 6-18 month contracts rather than in a permanent full-time capacity until they've worked up a reputation with the company.
To address one of your own comments above, it's not expected of developers to work on open source projects in their spare time. However, most of the best developers I've known already do this because they are so passionate about what they do, it is a hobby and career for them, not just a job. The nature of the high tech industry changes rapidly, and it's not uncommon for devs to have to retrain themselves, learn new technologies, and read a ton of books on a regular basis. If these points come across as "cons", I would strongly urge you to reconsider game development as your next career move.
In most countries, game studios (or software development companies in general) get thousands of resumes and CVs thrown at them every month. Many such applicants have a degree or several, advanced training certifications, years of proven experience with another company, open source development (which can be proven easily enough), beaming references from principal engineers and directors, the list goes on. It is a very competitive industry.
Finally, how experienced as a developer are you? You've worked with a company for one year, so that's good. Did you study software development in university? What languages are you familiar with? C++, C#, openGL, etc, are useful technologies to know in general in that field, but it will vary from studio to studio. How "highly specialized" is your current company, and what kind of work have you done? Can you:
- write a bug-free 20,000 line application?
- or track down bugs in other people's code with GDB and valgrind?
- accept that you won't necessarily get to work on games of a genre you enjoy?
- accept that you might be tasked with working on a graphics or audio or AI engine, and won't even realize you're working on a game?
There are a lot of "what ifs" you'll need to answer for yourself (please post an update to your question later) which would make a hiring manager discard the CV very quickly. If you've already got a good chance at signing on with "actiongames", congratulations.
After reviewing your edits, I'm going to say this career likely isn't for you. The two year stint in the military alone looks very bad, as most people are typically in it for at least 5-10 years, and a two year duration might suggest not knowing what you want to do in life, or a dishonourable discharge, at least in North America. I don't know if your country has a mandatory enlistment period for all youths. I recall Germany having something like that, so if it was involuntary, that's fine.
I'm curious as to why you weren't qualified to study IT. Did you not have the necessary grades in secondary school to get into a technical institute to extend your knowledge? Also, if it equates to two-thirds of a Bachelor's degree, it's probably less. A BEng or BASc in computer engineering throws in economics, ethics, law, advanced math and calculus, physics, chemistry, professional practise applications, etc, in addition to mountains of development work. Did your program provide the same?
If you think you'll enjoy the job at "actiongames" and it pays well, go for it. Nothing I can do to stop you. I will say that you are in your mid-twenties and do not have what appears to be significant training in any particular field. Straighten out your life ASAP and figure out what you want to do. I see 22 year olds come out of university every few months with plenty of experience from coop and practicum programs. It will be very hard to compete with that at age 30 with no formal training and not enough specialized training.