I cannot answer the question but I would consider the following:

(i) A Chase UR night is not an IHG rewards club night. Given that the UR rules should be applicable. I suspect that this night is treated by IHG as a night booked by an OTA or a night on a specific corporate rate (UR rate) and is a paid night, albeit you are not getting points.

(ii) To my recollection nothing in the rules prevents you from getting the Ambassador benefits on a third party website booking as these benefits are not linked with the booking channel. According to the rules however most benefits must not be granted on an IHG reward night (but several hotels will grant these), however we are dealing with a different animal here: Your night is not a IHG rewards night.

(iii) Contacting the hotel will to my belief not result in any useful information as the John Doe Booking Agent will have no clue about UR rewards nights.