9 AM to 11 PM in UTC+3 (Qatar), the times that are reasonable for playing assuming a 2-hour game, are 1 AM to 3 PM in my time zone and 10 PM the previous day to 12 PM on the West Coast. Most of these times shouldn't conflict with American football except for early afternoon games. (I don't know if Qatar had 9 AM games, but I know Olympics events often start that early). In fact, they can fill what would normally be dead times. Given that you say that FOX only did it because they were required to, they probably got higher viewership during the morning hours than they would if nothing was going on and didn't lose out on PM American football coverage.
Am I missing something? Not following the NFL or college football at all or even watching TV, I probably am.