No species is a sure thing to “fill the niche if humans disappear.” All contenders have some characteristics that make them more likely, and other characteristics that make them less likely to succeed. A lot will depend on the environmental conditions present when humans hypothetically disappear, and no doubt luck will play some role, too.
Raccoons, for example, have intelligence on par with cats and although they lack opposable thumbs like primates, they do have more dexterous hands than cats. But, cats outnumber raccoon >~20 to 1. Could raccoons gain the upper hand over cats? Maybe, but I don’t believe so.
Primates certainly have a greater brain-to-body ratio and intelligence than cats, but all of the great apes are endangered. Could, for example, chimpanzees expand and gain the upper hand over current broad-range species to attain world dominance? Maybe, but I don’t believe so. Remember, if the extinction of humans takes pressure off chimps, it also takes pressure off of their predators (e.g. leopards). Cats have a broad range of habitats (they’re present on all continents except Antarctica). Chimps would need a lot of luck to expand that far and wide.
The fact that the human population ~70k years ago dwindled to a few thousand before becoming the dominant species does not equate to chimps being able to do the same. For one thing, humans could have easily gone extinct at that time; their survival wasn’t a given and involved a degree of luck and conditions that may not exist today. For another thing, humans 70k years ago were more intelligent and more adept at tool-making than current great apes and therefore better able to defend themselves against predation.
And, of course, there are other species to consider with relatively high intelligence and/or tool usage (e.g. octopuses, orca, porpoises, sea otters, crows, etc.), but they have their own obstacles and limitations to contend with in order to replace humans as the dominant species.
My position is simply that cats may not be the best at any single qualification, but they have a formidable combination of qualifications that make them prime contenders for world domination in the event of human extinction (i.e. broad range, relatively high intelligence, adaptability, speed, agility, effective hunting skills, and solid and growing current population).
The family of felines has a proven track record of evolving significantly to fill a variety of niches (including alpha predator in various habitats). Sure, to become effective tool makers they would need to evolve more dexterous hands, but the current front paws of house-cats already show signs of proto-advanced dexterity (more so than dogs, for example). It’s just a hop, skip and a jump for them to evolve opposable thumbs.
I believe house-cats would also need to evolve into a physically larger sub-species in order to dominate. But, again, the feline family has a track record of producing large dominant species, so this should not pose a problem.
The future world language won’t be English, or Latin, or Spanish, or Klingon—it’ll be Meowish. I’ll bet a bowl of Kit & Kaboodle and a gram of Catnip on it. 