Video game is much more wider thing than drawing. It needs the game idea, an incredibly amount of definitions what happens in the game, object geometries, functionality and physics definitions of the objects and finally the visual appearance. Game development platforms help to keep the underhood things in control, but defining them is still the major task. Top games are group efforts where a small subgroup does the big decisions and most members do the hard detail work.
About drawing: Take a pen and paper and start. You must learn to sketch your ideas (no even a coarse sketch = no idea). Develop your skills at the same time (work out tutorials, try to copy something). Doing it in software is a parallel project. On line schools can help substantially, but they are not free.
Software: We cannot push commercial stuff here. Photoshop has got its position by solid performance, consistent user interface and support of CMYK printing. Many of us see its premium cost justified. I recommend freeware. Start with something simpler than GIMP (for bitmap images) or Inkscape (for vector graphics). My personal opinion: Start with Paint.NET and bitmap images. Get GIMP and some vector graphics program after you start to find by yourself the limits of Paint.NET.
If you are up to the task, you can in a couple of weeks learn enough software usage to make easily your own version of your example image from scratch. Try to make it clear how the image differs from a photo or photo realistic painting. You see that it can be put together by layering simple shapes (see NOTE1). Draw them and stack them and it's done.
But that's totally useless if you cannot catch your own ideas, so start with a pen and paper.
NOTE1: It's no shame to use clipart shapes or to modify a photo to get some needed shape as long as you use free to use or properly purchased stuff. Beware pirating images if you are going to publish (=sell or put visible or downloadable for free) something.