I agree that the feeling of free will is the mind projection bias, but I think we can make things simpler and less arbitrary by applying it to ourselves rather than rivals. It goes like "Why do I think I have free will? Because I cannot predict what I will do next. Therefore I am unpredictable." So "feels like free will" would be a property of any chaotic self-reflecting being with the mind projection bias.

This can be extended back to define free will itself with the additional stipulation that free will is defined as the stuff that makes you feel like you have free will. Some people definitely reject this additional stipulation, but I think the other options are silly :P