You can not create relative clauses without a phrase/Objekt/Noun etc. Because you need an object to describe it again.Actually relative clauses are side clauses(supporting clauses) that you describe the subject in main clause.
So lets 's split your sample sentence into two parts:
Bu bir kitap.(This is book.) - Ben bu kitabi okudum.(I've read this book)
Bu benim okuduğum kitap.(This is the book that I've read.)
As you can see you build relative clauses to make main clauses more explicit,more comprehensible.
In "Bu bir Kitap" as you suppose Kitap is not subject or object, however it's a noun predicate.
But in "Ben bu kitabi okudum." the word Kitap is an accusative object.
In short there is already no subject - object agreement in your example sentence. Because you don't re-describe I(ben), you describe just Kitap(book).
I've answered your question as a native Turkish speaker from Turkey.