Agent Smith pretty much Stuck his hand through my chest.

What's important here is you make a game, not that you land a job at a company making a game. I don't know if you've ever made a game before but its hard work, it took me over a year of part time programming to remake Solitaire, but its the best damn Solitaire game out there.

Take your time and don't look for what gets you results the fastest, that's how a manager thinks and its not how a game developer who wants to learn how to make games should think. I once spent a month just writing code without running the UI portion of the game, it was just log outputs to make sure the building blocks of what I was working on was solid. A good game developer should be able to love the code they are working with, or hate it enough to show it whose boss.

If you want one example of what you could do to get your feet wet, take any open source game on GitHub that is out there, and try to build and run it. Quake is a good example, go through it and see if you can compile it using Visual Studio. Learn to roll before you can crawl, and see what you will be getting yourself into, it's a beautiful thing. There once was a time where people would learn how to make games by writing mods for their favourite game, this could be a good chance for you to learn how some of your childhood fav's were made.

If you just want to make a game and you're looking for the fastest path to screen, I agree that web development is most likely the fastest, but then again……its web development.

I don't consider myself a game developer, although I have created multiple 2d and 3d (raytracing and rasterization) engines.

It's all about learning a programming language at a deep level like c++, some books that can help you understand the math, and having a great architecture for a codebase that is going to become vast. This will give you a great start.