I used one of the i5 CPUs with HD2500 integrated graphics in my main gaming PC for several years, up until only about 3-4 years ago. The performance was OK for me, but I paired it with a much newer, discrete GPU. Those integrated graphics are really going to hold you back. In games from 2012-2014 (around when those CPUs came out), they average 20-40 fps on lowest settings.

You don't have to use Steam, but it is a very painless way to play games that you own on Steam. I use Lutris for my non-Steam Windows games. It works well on my main gaming PC, but I often have issues with it on my laptops which have older integrated graphics, due to lack of Vulkan support, which Lutris seems to insist upon even when the software can use OpenGL.