After taking the liberty to consult the source you provided and doing my own research on the topic, I have firstly concluded that this claim is very opinionated, and is not backed by any definitive proof or evidence. The source that was sighted, the New York Times, is typically a very unbiased source, however, it specifically states at the top of the article that it is an opinion piece, and therefore not backed by any actual scientific evidence.
Additionally, all the further research I was able to conduct were strictly opinion based articles and biased towards either cats or dogs. There isn't any actual scientific evidence that I have found to support whether cats or dogs make better companions. The "better animal companion", whether that be cats, dogs, or some other species, is strictly based off preferences and what works for one's own lifestyle.
I have attatched links to websites comparing cats and dogs to further explain the point that it is very perceptive, and the companionship of cats and dogs is strictly based off preference with no actual scientific evidence to back it up.
https://www.diffen.com/difference/Cat_vs_Dog
https://www.hillspet.com/pet-care/new-pet-parent/choosing-between-dogs-and-cats?lightboxfired=true