Notice how Zoée first points at the book, then nods when she signs MINE. The nodding makes this more of an affirmative simple statement.
Some people wonder when it's approprate to use MY/MINE instead of ME/I since sometimes people will use ME/I for ownership (such as MY NAME). I like to explain it like this: if you can actually *touch* it - it would be appropriate to use the MY/MINE sign. If it is something that cannot be touched, like a name - it makes more sense to use ME/I.