Near the end of the article they suggest more study is required, and they state specifically that one shouldn't come to conclusions about cause and effect. They further state that it's possible some people are already in a good mental place, and thus are better able to look after pets.

I know anecdotal accounts are nearly worthless when it comes to making conclusions, but I can tell you as one who is near the age group involved, that I just got a kitten this past summer. I have never laughed or smiled so much in a long time. And the stark differences between my mental health pre-and-post kitty are profound. I had no idea how dark my life had gotten until he came along.

The article mentions isolation as being a contributing factor to dementia, and so this makes me wonder if the fact that you are now once again responsible for a life plays a contributing factor. Human beings need connection, whether it's person or pet. Having that positive connection has been shown to be helpful for one's health in other ways. Wouldn't surprise me to learn that pet ownership can prevent dementia as well. But…we need more data.