There are couple things you can do to make the computer seem a little faster.
SSD - Determine how much space you need before buying one. SSD's are very fast and most people put the operating system and their games/applications on it for quick loading. I use the Crucial BX100 2.5" 500GB SATA III to store my games and you can get them up to 1TB in size. There are other brands worth considering, like Samsung and Intel. You may need an adapter or bracket for your PC case to convert the 3.5 inch slot to a 2.5 inch one for the SSD, the Rosewill RXC200M or something like it would be good. Once you get it, move the OS and games onto the SSD and leave the traditional platter-based hard drive you have now for media, like music, movies, pictures, etc.
GPU/PSU - You could also get a new graphics card with a new power supply, but I doubt this minitower case could easily accommodate one. If you go this route a 500W Corsair power supply with an Nvidia GTX 950 graphics card, or a 960 if you can get a good deal, would be the level you would want to aim for
I would go with an SSD, especially if your son is happy with the performance as it is now once he is in a game. The SSD will affect almost everything loaded onto the drive, so non-gaming activities will benefit.