"A good sight-reader's skill is not the ability to read more notes than everyone else, but to read fewer."*
In a not-so-distant past I myself was given to marveling at how great sight-readers could see so many notes at once and play in tempo. How was that possible? In short: It's not.
An accomplished sight-reader does not see all the notes. Through experience and practice he or she has assimilated a body of skills and knowledge -- in music theory, analysis, style, piano technique -- such that allow them to infer learned patterns and make assumptions based on sparse indications (key notes and other markers) in the score.
A parallel can be made with an average literate adult. A person who can fluently read this blog post isn't so much someone that's particularly talented at seeing a lot of letters, as someone who has learned to instantly recognize and make sense of the patterns of written language.
* Pascal Le Corre in La Magie du Déchiffrage, p.97. "La compétence d'un bon lecteur n'est pas de lire plus de notes que tout le monde mais, en réalité, d'en lire moins !"