Learning the basics of programming and how to build a web application is a good idea. I suggest getting a basic understanding of it under your belt and then looking for libraries and frameworks you can use. I would not recommend trying to build your own engine completely from scratch unless you're really in it for the long haul (i.e. years, potentially, assuming you're starting at square one with learning programming).
The apps you mentioned are text editors, and they're a good place to start. They're just like any other plain text editor, and you just use them to write code. You'll write various files, a main html file, one or more CSS files, and then some JS files, some of which will likely be libraries, while others will be your code. In the main html file, you'll "link" to the other files using html elements like <link> (for CSS) and <script> (for JS).
To test your code, you'll run the html file in a browser. I recommend downloading some examples to show you how to fit everything together.
All that said, the simplest solution would be to get your hands on a computer that can run a more standard OS. I don't think you'd need to break the bank, either, but I don't know how feasible that'd be for you. Reinventing the wheel doesn't seem like the more cost effective solution to me; I think you'd be surprised how much work goes into even a simple text-game engine.
Getting your feet wet with some general programming in the meantime is probably still a good idea, though.