Can someone acquire an expert programming level and a master game developing skill on his own in order to pursue his career as a successful game developer or software programmer?

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It all depends on your ambition and aptitude!  I taught myself a couple of languages and developed a couple of my own games...still in development after 3 years (including a year hiatus).  So there's something to consider: it will most likely take longer for you to teach yourself than to have someone (like an experienced collaborator, company training resources or other instruction) show you some of the tips/tricks/techniques that would fast-track you to your goals (relatively speaking). There are some questions you need to ask yourself: Do you want to work as a designer/developer/coder for a software company or do you want to freelance?  Do you want to work on games for mobile platforms like Android /iOS or PC-based?  Do you want to build a game using an existing Open-Source engine or make your own engine (this mostly applies to the freelancing option)? How patient are you when it comes to taking each step to achieve your goals? You may make a living as a software engineer for gaming, but unless you own the company, you will probably have a tough time affording a Lamborghini, even as a freelancer. Either way, there is no harm in at least attempting a project on your own, just so you can see what you are getting into, and you will undoubtedly learn a few things along the way that will help you when you collaborate or land a position at a company, if that is the route you choose to pursue. Thanks for the A2A and I wish you the best!

You're actually mixing two distinct objectives: being successful and being an expert. If you want to be an expert, you need to have a lot of experience. Now, your path here can vary: you may become an expert in independent development without joining any companies, on your own by working a lot independently. Or you can work a lot with teams and become an expert in team development. To be successful, though, you need to pursue different goals, not exactly related to team or independent work. You need to do the things that are the most valuable and lead you closer to your goals. I won't specify what goals - success means that you achieve your own goals that you set for yourself. But being an expert is hardly a worthy goal in this respect.