Gods are "constructs of our imaginations" too, so you're right that the claim is somewhat trivial. We imagined gods as projections of ourselves, so naturally we're better at fulfilling that role than other life forms that lack those projections.

But more precisely, personhood is more godlike than animality or planthood because of the combination of consciousness, intelligence, and autonomy which makes for a levelling-up of creative outputs, as in terraforming. We're not so limited by evolutionary niches because we reshape the environment and thus create our own opportunities. Animals and plants lack that self-determination.