A Question: is it possible for me to create an AI that learns to play games which I did not create?
As far as I know you might archieve this with Reinforcement Learning. But there are some limitations in this approach: You have to train your algorithm a long time for even learning to press a button. The second limit is that you have to define the possible actions, that the agent might choose. And remember: Every single thing your system has to learn will affect your training time. 

You can dive into this topic by searching for the openai gym, which will give you a good overview about what is done right now in order to build AIs which play games. A good book about this topic is Reinforcement Learning - An Introduction by Barto and Sutton.