Yes, cats have knees. The position of the cat knee is shown below in the picture. The philosophical question is whether cats have knees and elbows. I think the answer should be simple. As cats have legs and no arms then they have four knees rather than two knees and two elbows.
Some people ask whether cats have legs and arms. I think it is impossible to say that the cat has arms but perhaps a visitor will have a different opinion. If we say that a cat has arms and therefore has elbows we are, I would say, anthropomorphising the domestic cat. We like to do that. It is understandable.