Dogs help reduce cognitive decline?

Saw this facebook post by fitness influencer Dan Go.

Dan cites this paper, and claims that research shows "pet owners who live alone have significantly slower rates of cognitive decline".

He goes on to say (his main claim), that dogs specifically are the best pets for this purpose. Because dogs help us to take walks, socialise, and follow routines.

This all sounds logical enough. However, the paper cited doesn't actually differentiate between pet types. (Respondents were just asked whether they had a house pet or not.)

That means Dan's claim about dogs particularly, are not backed up by the paper he cited. It could of course come from another study he didn't mention.

Also, the paper's actual findings (that pet owners have slower rates of cognitive decline), only applies when comparing between people who live alone without pets, and people living alone but do have pets. Owning a pet didn’t make you better off vs if you lived with other people.