I'm having the same issue, though it is limited to my iPad. When browsing any of the individual property sites, anything I click on (including when trying to make a reservation) will open up a new Roomkey tab; meanwhile I get a blank screen on the browser window that I was using for Hyatt.com.
So basically, I cannot use Hyatt.com on my iPad's browser. This is something that just popped up a week or so ago.