Earlier quoted context omitted.
I mean, there are pretty objective things to test for. Object permanence. How many things can they keep in working memory? How many steps can they work through linearly to an objective? How many dependent elements of a puzzle can be branched off for a single step? Can they understand symbols as being representative of objects? Of verbs? Adjectives? Can they understand counting, grouping? Can they extrapolate solution…
One overriding question may be: Do they need to? There are things that other animals can do which humans can't, such as an octopus communicating with a grouper fish, two entirely different species, by changing the color and patterns of their skin, to corral and trap a prey (as seen on a segment of BBC's Blue Planet.) Are humans "dumber" if we use that objective criteria to compare intelligence?
We have advanced communication with our domesticated animals, especially dogs. Also have some communication with non domesticated animals like primates, dolphins, etc..