From the linked Hyatt page on that Reddit post (also reachable from the Hyatt front page via hamburger menu > Loyalty Program > Earn and then scroll down to Airline Partners)
World of Hyatt members can earn miles with one of the airline partners below per eligible stay at a participating Hyatt hotel or resort. Simply present your airline partner and World of Hyatt membership numbers at check-in. Set your earning preference at the hotel’s front desk and avoid having to present your travel partner membership number to earn miles every time you check-in.
It does seem weird that there's no way to do this yourself via the website or app, but maybe give this a try on your next check-in? i.e. if they can switch you from earning Hyatt points to airline miles instead, then hopefully they can switch it back as well.