While the poem was written as a single, continuous piece of text, it wasn't printed as a "book" in the modern sense until much later. The earliest surviving manuscript of Beowulf dates back to the 10th century, and it was likely copied and passed down through generations before being bound into a book.
So, to answer your question, Beowulf was not written as a book because the concept of a book as we know it didn't exist in the way we think of it today. It was originally written as a poem, and only later was it transcribed and bound into a manuscript, which eventually became known as "the Beowulf manuscript."