Intelligence can be defined as the ability to accurately predict the future consequences of one's actions. And the only way to make such predictions is by having an internal model of how the world works.
Moreover, for social species that live and evolve in groups, like humans, this world-model must crucially include a model of oneself and other minds. We need to be able to predict how others will think and react to our own behaviors. This is what gives rise to self-consciousness and "theory of mind" - a world-model that is recursive and includes representations of itself.
That said, while our conscious experience seems deeply linked to our world-model, the world-model likely encompasses much more than just conscious awareness. It runs in the background, guiding our reflexes, breathing, balance, and myriad other functions below the level of consciousness. It takes in raw sensory data and interprets it, and uses feelings and emotions as a communication channel to influence conscious thought.
There are known critical developmental windows during which an animal's world-model is shaped by early sensory experiences and social interactions. If key stimuli are missing during these windows, the world-model may remain stunted in certain ways even if the missing stimuli are later provided. The animal may compensate through other means, but its overall intelligence - its ability to model and predict - will be constrained by the limitations of its world-model.
So in that sense, a highly sophisticated but narrowly specialized world-model, as in a mathematical or musical savant, may produce an individual who is brilliant in one domain but quite limited in general intelligence.
Whereas a broad but shallower world-model, as in many animals, can enable robust if limited intelligence that is well-adapted to the animal's ecological niche.
Evolution tends to select for world-models and intelligence that are "just enough" for an animal's lifestyle and no more. The metabolic cost of excess intelligence makes it maladaptive. So we see each species with a world-model and associated intelligence that is tailored to its particular environment and survival needs.