I'm guessing that the cafe idea is intended for people who love cats but are unable to keep them at home. I don't know about Japan but, in the United States, it is difficult to find a landlord who will rent an apartment or home to someone with a cat. Before I was able to buy my own home, I had a lot of trouble finding a place that would take my cats, and was once evicted from an apartment because I didn't tell them that I had a cat, and my cat insisted on sitting in the window.
So I can appreciate that it might be relaxing for a cat lover to sip tea and play with cats, particularly if the cats are well socialized, as I suppose they are. I like dogs, but have never owned one, so I enjoy visiting people who have dogs sometimes. Of course, it depends on the dog, as some of them are simply annoying.
