Hi, as a web developer, you could also look for one of the Javascript and HTML5 game frameworks.
For small games, HTML5/Javascript is really surprisingly fast nowadays.
A friend of mine who is a veteran game developer recommends Pixi JS. I have never tried it personally but it looks very impressive.
I personally use Game Maker but I am not sure I would recommend it to you due to its peculiar programming language. However, if you are willing to learn a custom programming language that you probably won't use anywhere else, one good side of Game Maker is that it lets you write nice 2D games without having to learn a huge amount of things. In a way, it's the best engine I found that lets you code games how they were developed 30 years ago and that is a very good thing to get started in my opinion.
You can move to Unity or even to c/c++ later when you are more experienced.
Oh, I was forgetting... if you wanted to learn how to make c/c++ games one great resource is handmade hero. Look it up on youtube ?
Good luck