The third eye that Khan possesses was not a naturally achieved one. Originally belonging to the ancient race of the Guardians, they have natural mental prowess and incredibly high intelligence standard.
In other words, they are a race that is governed by great science and logic. In order to attain a higher form of intelligence, they got rid of most of their emotions to give way to their logical advancement which eventually led to their incredible scientific and technological breakthrough.
But in return for their overwhelming mental breakthrough is their loss to their soul's true capacity.
Unlike the Guardians, Khan's own Arkhan race diverted to a different track which depends more on the use of the technology and logic. Using advanced technology and the thousand years old knowledge they have accumulated, he managed to find a way to get the same power as if having a third eye.
