The important thing here is not what the Spanish "phrases" say, but the words shown and their relationship to each other. Their structure. What the "phrases" say is irrelovant. Though we do need to understand what each means, and whether meaningful or not. And the many ways it could be said in English is a waste of one's brain power thinking about it.
I agree that this is a poor translation, it gives me "she is reading me one menu", I can't think of any scenario where you're given more than one menu at a restaurant so "She is reading me the menu" or I guess if you're just reading random menus (for fun?) "She is reading me a menu" would be OK