This got me thinking as well, if it's on the other shoes, Otto got cut and bloodied, I think the referee are going to stop it and won't allow it to go to distance. But since it was Tyson Fury who got the injury early the referee or the doctor itself let the fight continue.
There are news specially coming from Frank Warren, that the Wilder fight me be delayed because they want the cut to be fully healed.
Anyway, this thread should be lock by the OP. The fight is over now.
The champion will almost always get the benefit of the doubt in a boxing match, that's just how it goes. The referee knows that Tyson Fury is an experienced boxer, and probably knows more than him about how his body is operating and what to do in that situation. Of course, when it comes to a less experienced fighter they might not have this knowhow, so they would be more inclined to stop the fight.
There was a similar cut in the recent fight with Badou Jack against Marcus Browne, though this cut was deeper and above both eyes, making it very hard for Jack to see. The referee called an early stop to the fight after a couple of rounds and it went to decision where Jack lost.
https://youtu.be/VebwIrJNz-QCorrect, the champion always get the benefit of the doubt, specially with names like Tyson Fury.
I also remember Vitaly vs Lennox, Vitaly was cut badly, they should have stop the fight then. But Vitaly continue the ring doctor finally stop the fight because of the severity of the cut. However, that injury Vitaly had haunted him for the rest of his boxing career because that cut didn't fully heal and he was easily busted after that one.
Good call for Warren to heal first the wound, but I don't know how long it will take it though. Because they seems to announce the fight will Wilder next year Feb 2020.