The 2nd verse of Baqarah say: "this is the book", But wasn't the Quran sent down as a "revelation"?

Al-Qur’an literally means ‘The Recitation’, and is an excerpt from the Book of Knowledge, Book of Records, Book of Nature or Master Plan – an allegorical representation. The Quran is a compilation, an explanation, and a reading within, and of, this Book 85:21 in fact, this is an exalted, sublime compilation and recitation (Quran) 85:22 within the preserved, imperishable tablet

This needs to be understood along with other verses as well. 10:37 And it was not for this Quran to be produced by other than Allah, but [it is] a confirmation of what was before it and a detailed explanation of the Book, about which there is no doubt, from the Lord of the worlds. The Book (of Nature), about which there is no doubt, is explained via prior revelations, and culminates within the Quran.

12:1 These are the signs of the clear Book 12: Indeed, We have sent it down as an Arabic (clear, plain, distinct) Quran (compilation, reading) so that you may understand 13:39 Allah eliminates what He wills or confirms, and with Him is the Mother of the Book. So umm-ul-Kitab is the mother of the book (Book of Records, Book of Nature or Master Plan) with Allah. From it is comes the revelation to the prophets; thus, the Quran is the collection, compilation, explanation and recitation of it.

Allah says:

ذَٰلِكَ الْكِتَابُ لَا رَيْبَ ۛ فِيهِ هُدًى لِّلْمُتَّقِينَ

THAT is the Book, no doubt in it, a guidance for those who have taqwa. (Quran 2:2)

"That", as opposed to "this", implies something distant.

Allah says:

ذَٰلِكَ الْكِتَابُ لَا رَيْبَ ۛ فِيهِ هُدًى لِّلْمُتَّقِينَ

THAT is the Book, no doubt in it, a guidance for those who have taqwa. (Quran 2:2)

"That", as opposed to "this", implies something distant.

إِنَّا جَعَلْنَاهُ قُرْآنًا عَرَبِيًّا لَّعَلَّكُمْ تَعْقِلُونَ

Indeed, We have made it an Arabic recitation so that you understand. (Quran 43:3)

وَإِنَّهُ فِي أُمِّ الْكِتَابِ لَدَيْنَا لَعَلِيٌّ حَكِيمٌ

And indeed it is in the Mother of the Book with Us, Exalted, Wise. (Quran 43:4)

My question is, why is this Ayat referring to Quran as a book?

This needs to be understood along with other ayats.

In Surah aali Imran 3:81 =

And when Allah took the covenant of the prophets, [saying], "Whatever I give you of al-Kitab and wisdom and then there comes to you a messenger confirming what is with you, you [must] believe in him and support him." [Allah] said, "Have you acknowledged and taken upon that My commitment?" They said, "We have acknowledged it." He said, "Then bear witness, and I am with you among the witnesses."

In surah Younus 10:37 =

And it was not for this Quran to be produced by other than Allah, but [it is] a confirmation of what was before it and a detailed explanation of al-Kitab, about which there is no doubt, from the Lord of the worlds.

And in surah ar-Ra'd 13:39 =

Allah eliminates what He wills or confirms, and with Him is the Mother of the Book.

So al-Kitab is the mother of the book with Allah, and from it is what all the revelation was revealed to the prophets, and the Quran is what explains the revelation.

In English a book means the literal meaning that we all know:

A book is a set of written, printed, illustrated, or blank sheets, made of ink, paper, parchment, or other materials, usually fastened together to hinge at one side.

However, in Arabic a book can mean many other things:

• manual ; record ; register ; textbook

• a copy of the (Holy) koran

• letter ; message ; note

• book ; compilation ; publication ; volume ; work ; writing

• elementary school ; school

• a primary school

• institution for educating pupils

• a shool for educating the little children

In the context of these verses koran means a guide:

in it is guidance sure