Apple Watch compatibility with iPhone always ties to iOS versions, which is tied to iPhone generations. I do agree that it is better to let salesperson ask what generation of iPhone they are using before recommending which Apple Watch to buy.
You can always return that new Apple Watch to Apple and buy something else for your wife’s Christmas present. To me it makes no sense to keep a brand new Apple Watch that is not compatible with your iPhone X, nor it makes any sense to buy the latest iPhone just for Apple Watch compatibility.