Dave Meltzer reports that there were alternative plans for the match discussed last week after the decision was made that the show would continue as scheduled.
At one point, the plan was to tape the match ahead of time and then insert into the broadcast on the WWE Network. At another point, there was talk of doing the match live at a technology center near the Performance Center. The idea was that if they did it live, they could make it look like the match was taking place in Saudi Arabia or they could do an empty arena match. Only the people at home watching on the WWE Network, not the fans in the crowd, would know that the match was happening.
The problem is that if they did the green screen or the empty arena match then it would draw more attention to the fact that Bryan was refusing to go to Saudi Arabia and it would be difficult to do an empty arena match with no fan reaction. It would also look bad on the company if media outlets picked up on WWE trying to fool the fans at home. More negative media attention is the last thing WWE wants right now.
In the end, WWE management decided to have Bryan lose on SmackDown Live and then have Joe run in to set up a match with Styles at Crown Jewel. Going into SmackDown Live, everything was kept a secret from everyone except a few people and the format sheet just listed a "match" going through two segments instead of listing who was in the match.
Styles won the match clean with the Calf Crusher. It's not known if there is heat on Bryan for pulling out of Crown Jewel but it is unusual for a top babyface to lose clean via submission.