Note: Many people may not understand this answer as it describes here Islamic theology, Theosophy, Higher Science.
"knowledge from the Book" is the knowledge of the "Mother Book" that is with God. This Book has been written by the noble angels those are closest to God. And the language of the Book? Nothing but a signal in the form of "FREQUENCY"
God is so Holy. It is because God need not to say anything as He is so Holy. Then how God instructs angels? The angels and the scribers of the book and those nearer to Him understand what God wishes with the signals they receive. And they received it in the form of frequency. And the Scribers placed the instructions in its proper place exactly in the form they receive it. Every creation thus connected with the Book of God. Thus it becomes true God says "Be" and it is. Do you Understand how the word "Be" creates a matter or a living thing? Actually, word "Be" contains some frequency, and the amount of energy that each frequency contains bonds a no of atoms to form a thing.
The Mother book is actually contained whole creation in the form of frequency. Matter created by atoms is a half truth actually proved false now. As Quantum Physics states Matter never created without energy in the form of frequency that needed to bond atoms to create a molecule of the matter. Thus we can say everything created by frequency.Those have knowledge of the Quantum Physics understand better what I am saying. [see my article for a better understanding-
Quran sent down from the unseen world ie from the mother book to the real world in a night of decree. Language? As God need not to say anything, So the language of God, is nothing but signal, in the form of energy and "FREQUENCY" and that frequency sent down from the mother book to the sky of the 4th universe of the real world. And From there angel Gabriel brought that to the heart of Muhammad as necessary basis. And Muhammad understood that in his own language.
As the whole Quran sent down in the form of frequency, so it needed to protect from Jinns, the spirited creature, who have knowledge of the creation ie. knowledge of the frequency. [for a better understanding of Jinns- see my article- https://faruquez.blogspot.com/2016/10/dark-art-history-of-origin-of-black.html]
What we are going to say, "knowledge from the Book" ie. who have knowledge of the creation or in other words knowledge of the frequency. Thus the Jinn brought the Throne within a sec. from a distance more than 2000 miles. How? simple. He just need to know the exact shape and to create the bonding frequency of the materials within the shape.
Now for the case of "knowledge of the Scripture". ie. knowledge of Torah, Jabur, or Gospel. Now Who have pure knowledge of Torah?. Obviously it is Moses. Similarly, knowledge of Jabur?, it is David, knowledge of Gospel?it is Jesus.
And who have knowledge of the Scriptures? Those are Muslims, because they have uncrroupted Quran, the last of Gods Scriptures, which includes an uncorrupted form what was in those scriptures. Why Quran Include those? Because Muhammad is the seal of the prophets, ie no chance to have a guide from God ever after except the last scripture. if the previous scriptures shall Corrupt ever. But we know a scripture shall never come if the previous not corrupted. As quran the last, surely the previous one is corrupted. Then how they will be guided to the right path. Through Quran, which is the way of Mercy for them, and thus quran needed to include what is in those scriptures in a corrected form. Thus Muhammad is the Messiah of Mankind as he brought mercy to the mankind. [see my article-Muhammad: The Messiah to the Mankind.]
Again, as Muhammad is the the Mercy to creation ie. Messiah to the Mankind, then all the prophets shall know him properly and the scriptures they bears shall manifest him. and when a scriptures corrupted then a new appeared. Thus if Quran is the latest then obviously all before it were corrupted.
So Quran says, due to corruption or their haughtiness if Jews and Christians reject Muhammad, then it doesn't mean anything because, Moses, David or Jesus those have knowledge of scriptures fully, they shall not reject him, but will be the witness of Muhammad in the day of Judgement. and they were promised to God to do it in their earthly life, Qur'an says-
And recall when Allah took a covenant from the Prophets: 'This is the Book and the Wisdom which I have given you. But should a Prophet come to you confirming that which is already with you, you shall believe in him and shall help him. So saying, Allah asked: 'Do you agree and accept to take up the burden of the covenant?' They answered: 'We agree,' He said: 'Then bear witness; and I will be with you among the witness. -[al-Imran, 3:81]
And actually that too not necessary because God himself bears witness of Muhammad and that states the verse that we are analyzing here.