They serve merely as a heuristic which an intelligent agent can employ in order to gauge intelligence. Making these "definitions" entirely circular since they depend on what they define in order to be meaningful!
This can be seen simply by looking at the properties of these "definitions" of intelligence and observing that none of them have anything to do with intelligence. What are these properties?
The point being that whatever makes an agent intelligent can't be the same thing that makes it an agent, otherwise there couldn't be stupid agents.
Is interaction a feature of intelligence? Are environments a feature of intelligence? Is success a feature of intelligence? No, they are not. Not individually and not in any combination. Intelligence isn't what something does, it's what something is.
And that fact is blindingly obvious to anyone of intelligence who has worked or known underachieving gifted children. But perhaps not to imbeciles who wish to deny the notion of gifted intelligence out of petty jealousy.
You see, gifted children are just as likely to become highly unsuccessful in life as they are to become highly successful. So they are "unsuccessful" in "many wide environments". Does this make them unintelligent? Hardly!
Are bacteria intelligent because they can colonize more environments than a human being? Is a single human being stupid because he or she cannot survive in any environment if left alone? Are a thousand idiots more intelligent than a lone genius? Yet this is what the "final definition" implies.
Clearly the standard approach to defining intelligence has deep flaws if it suffers from such trivial counter-examples. The fact these are never noted, let alone addressed, nevermind countered, marks the authors of such work as imbeciles.
Now obviously it's too much to ask an imbecile what intelligence is. Yet this is exactly the absurd situation we are presented with on that page. Definitions produced by imbeciles in a process of group-think. They are entirely unoriginal and the mere aggregation of them adds nothing to them.
Now, if someone capable of originality had been asked to come up with something insightful, they might get "living representation" or something else that would provoke deep thought. Something that has a chance of being right.
Followed up in a formal theory of intelligence.