Earlier quoted context omitted.
I would differentiate them in the following way: Product Engineer: Focused on creating something that fulfills users' need or want UX Engineer: Focused on polishing the product to make sure the user's need or want is fulfilled with the least amount of friction.
UX is not about polish. UX is the product -- literally, from the user's perspective. I don't think there is a meaningful difference between Product Engineer and UX Engineer.
A Product Engineer's job is to identify the 20 features because they are useful for users.