Around 40 years ago, a law has been passed that the members of The Committee for the Promotion of Virtue and the Prevention of Vice (The Religious Police) will oversee and force people on abiding by the islamic teachings. In doing so, the closing of shops during prayer time has been implemented, and there are no exceptions not the gas stations or even the pharmacies, the grand mufti at the time actually wanted the traffic to be stopped during prayer time but fortunately it has never been implemented.
There are other things that the religious police are used to do, like if they didn't like your haircut they will shave your head and make you write on a piece of paper that you won't do it again. They also used to seize and check your phone and ask for identification papers to prove that the women with you is your wife or sister etc... And they also used to have women wear a more modest abaya and prevent them from wearing aesthetics or they will have them get out of the mall, and overseeing gender segregation. They also work on seizing alcohol and spread awareness about drugs. And of course you can't have a religious police without having them hunt witches and wizards and dismantling magic.
The closing of shops was just a custom after Mohammed bin Abdulwahab (the term Wahabism was derived from his name) as in it was voluntary.
5 years ago the law has been revised removing the forcing part of the law and a year later the religious police has been stripped of their jurisdictions, they will have to just report to the actual police. But nothing have changed regarding the closing of shops, but after COVID19 and the instating of curfew and partial curfew, shops couldn't afford to close during prayer time, so they kept open even after the removal of the partial curfew, but still most of the shops close during the prayer time.
Interesting experience. Do you live there?