You’ll earn Hyatt points on your WOH credit card at the MGM properties at the same rate as if you used your WOH credit card at the Marriott. The MGM resorts are not coded on Chase’s system as a Hyatt Hotel.... as they technically are not Hyatt Hotels.
You’ll earn points on the room rate and room charges with elite bonus as applicable... but that has nothing to do with what credit card you use (or don’t use for that matter).