:salam2:
That translation can't translate properly, in the Quran, the written book was and is not in the earth, so when there is kitaab it is referring to the wriiten book with Allah subhanna watalla. It never says written book meaning Quran it says that which is brought down and says it is the Quran or implies it as revelation.
when you look for meanings see where it says kitaab, that means book while Quran means that which is recited.
The second ayah of surat al-baqarah says the book but it also says that which is far away when it uses aoolaika. if it meant the what you are reading it would of said hatha.