All Books in the restricted area are there for a good reason. This book is there cause it's screaming.

Note that here the film is conscientiously replicating the novel of JKR

He had to start somewhere. Setting the lamp down carefully on the floor, he looked along the bottom shelf for an interesting looking book. A large black and silver volume caught his eye. He pulled it out with difficulty, because it was very heavy, and, balancing it on his knee, let it fall open.

A piercing, bloodcurdling shriek split the silence -- the book was screaming! Harry snapped it shut, but the shriek went on and on, one high, unbroken, earsplitting note. He stumbled backward and knocked over his lamp, which went out at once. Panicking, he heard footsteps coming down the corridor outside -- stuffing the shrieking book back on the shelf, he ran for it.

Harry Potter and the Philosopher's Stone, Chapter 12 (The Mirror of Erised)

There are other case of charmed books in Harry Potter's stories. Like "The Monster book of monster"

"How do we open our books?" Malfoy repeated. He took out his copy of The Monster Book of Monsters, which he had bound shut with a length of rope. Other people took theirs out too; some, like Harry, had belted their book shut; others had crammed them inside tight bags or clamped them together with binder clips.

"Hasn' -- hasn' anyone bin able ter open their books?" said Hagrid, looking crestfallen.

The class all shook their heads.

"Yeh've got ter stroke 'em," said Hagrid, as though this was the most obvious thing in the world. "Look --"

He took Hermione's copy and ripped off the Spellotape that bound it. The book tried to bite, but Hagrid ran a giant forefinger down its spine, and the book shivered, and then fell open and lay quiet in his hand.

"Oh, how silly we've all been!" Malfoy sneered. "We should have stroked them! Why didn't we guess!"

Harry Potter and the Prisoner of Azkaban, Chapter 6 (Talons and Tea Leaves)

As @Bellatrix said, Spells on books seems to be quite common, and Madam Pince has been known to use all sorts of spells on the books in her library.

Though I have removed the usual library book spells from this volume, I cannot promise that every trace has gone. Madam Pince has been known to add unusual jinxes to the books in her care. I myself doodled absentmindedly on a copy of Theories of Transubstantial Transfiguration last year and next moment found the book beating me fiercely about the head. Please be careful how you treat this book. Do not rip out the pages. Do not drop it in the bath. I cannot promise that Madam Pince will not swoop down on you, wherever you are, and demand a heavy fine.

Quidditch Through the Ages, Foreword

It could have been a Charm cast on the book for its security.

Harry takes the book that started screaming from the Restricted Section after having snuck in under his Invisibility Cloak, without permission to be there or take a book.

“A large black and silver volume caught his eye. He pulled it out with difficulty, because it was very heavy, and, balancing it on his knee, let it fall open.

A piercing, blood-curdling shriek split the silence – the book was screaming! Harry snapped it shut, but the shriek went on and on, one high, unbroken, ear-splitting note.”
_{^{- Harry Potter and the Philosopher's Stone, Chapter 12 (The Mirror of Erised)}}

Spells on books are possible, and Madam Pince has been known to use all sorts of spells on the books in her library. It's very conceivable that she might have put spells on (some or all of) the books in the Restricted Section to prevent students from sneaking in and taking them.

“Although I have removed the usual library-book spells from this volume, I cannot promise that every trace has gone. Madam Pince has been known to add unusual jinxes to the books in her care. I myself doodled absent-mindedly on a copy of Theories of Transubstantial Transfiguration last year and next moment found the book beating me fiercely around the head. Please be careful how you treat this book. Do not rip out the pages. Do not drop it in the bath. I cannot promise that Madam Pince will not swoop down on you, wherever you are, and demand a heavy fine.”
_{^{Quidditch Through the Ages}}

No Canon Explanation.

I've googled this and tried to get every information I can have, and all I found is that this is a piece of book in the restricted section that screams (though the movies showed a different scenario: the book spawned a screaming face).

So theoretically, there is no such answer as to why this book screams. As for Pottermore and J.K. Rowling, there aren't any stated reasons as to why this book screams.

There is no explanation as to why it screams. JKR probably just put it there for the dramatic effect that a screaming book in a magical school would provide.