AI doesn't necessarily mean self aware, rather it refers to a computer's ability to do tasks that we often associate with human intelligence. The name Artificial Intelligence implies just that -- a "fake" intelligence. The ambiguous thing here is how you define a machine being intelligent, and that's often where people start to think of being self aware.
There are a lot of different types of AI, (with the connect 4 AI being a low tier trash AI), and with some of the more advanced AI involving deep neural networks.
It would be hard to even know if an AI was self aware because AI generally attempts to mimic patterns and behavior. The real question would become is the AI actually self aware, or is it just mimicking behaviors associated with being self aware.
But Idk, I'm just some dumbfuck on the internet with wet cat food in my brain.