I believe most people believe the cat was domesticated in Egypt, not Europe as the chart above says.
Humans did not domesticate the cat. The cat domesticated humans. I daily serve as a cat doorman, a cat foodserver and food provider, a cat chaser (stimulation), medical provider, ad infinitum. And I don't mind -- he keeps me greatly entertained.
There is a European Wild Cat (Felis silvestris silvestris) that looks just like our domestic housecat, but as I understand it, all attempts to domesticate it have failed. It's just too wild. The African Wild Cat is domesticable, and is assumed to be the ancestor of housecats.
Some years ago I had a friend who had a cat that he claimed was half Bobcat, half domestic. I don't know if such a thing is possible, but that cat actually looked like a bobcat/housecat hybrid, and it behaved like one, too. It was definitely not a purry, loveable lapcat, even though he had raised it from a kitten. It had longer legs than a normal housecat, too.
I believe you are correct. It is my understanding that all domestic cats descended from the African Wildcat, like the one pictured here:
I have also read that the domestic cat spread throughout the world so quickly because they took quite willingly to ships. Because of the rats that most ships were plagued with, sailors loved to have a good cat aboard who was happy to hunt rats all day down in the holds.