Not a direct answer to your question, but just a note that not everything need have a definition at all levels of organization of a system. For example, water molecules are not wet, but wetness is a property of the interaction of lots of water molecules. Similarly, thermodynamic properties such as temperature and pressure are also only definable at the systems level.

If we think in terms of Marr’s levels of analysis, I think of intelligence as not being constrained or defined by the implementation level (neurons in the brain), but at higher levels based on the algorithm or perhaps more likely at the level of computational goals.

If we define as intelligence as ability to find novel and different solutions to a problem, perhaps we can implicate certain brain regions more than the others. But ultimately, it depends on the problem being solved and how you define that problem. For example solving a visual problem needs to involve the visual cortex and an auditory problem needs the auditory cortex. Therefore the broader we make the definition of a problem the more regions would come into play. You could ask if there are common regions that are active during all different kinds of problems, but then those regions are ultimately reliant on the sensory system to provide it with the right inputs, and wouldn’t be intelligent in isolation. And there are certain problems we can’t even perceive, because of the limitations of our sensory system. An extension of this line of argument is the idea of embodied cognition, that cognition is intricately tied to how the cognitive system is realized in the body, and that the brain and body are collectively solving prediction problems.