ודרך הפשט ב"ספר מלחמות ה'", שהיו בדורות ההם אנשים חכמים כותבים ספר המלחמות הגדולות, כי כן בכל הדורות, ובעלי הספרים היו נקראים מושלים, שנושאים בהם משלים ומליצות, והניצחונות הנפלאים בעיניהם מיחסים המלחמות ההם לה', כי לו המה באמת.
And in the simple meaning of the "Book of Wars of G-d": In those generations, there were wise men who wrote about the great wars, as it is in all generations. And the authors of the books were called "Moshlim (parable makers)" as they would bear parables and lessons (ie. the lessons that are derived from the parables). And the triumphs that were wondrous in their eyes, they would attribute to G-d, because they were truly His.
I understand Nachmanides as saying that this type of book was a common thing for people of the time to write books about. And Jews wrote these types of books too. In fact, if you want more information about this war, you could check out the book that Jewish writers kept about the wars they fought.
So at least according to this explanation, I don't think it was meant to be a book of Tanach as much as a diary of national wars.