The X in UX is Experience so indeed a UX Engineer's role would be to improve the user's experience of the product not necessarily define what the product should be. It's unfortunate that UX is being confused with Product. Let me illustrate with an example: Consider a product with 20 features, 10 of which will be helpful to the user once they have been using the product for a while. The UX engineer's job is to identify this and provide a user flow of progressive disclosure of those 10 features based on user's actions. This improves the Experience for a user by not overwhelming them with all 20 features when they are just starting to use the product.
A Product Engineer's job is to identify the 20 features because they are useful for users.
