From the right? No we're not talking about giving way to traffic. We refer to courtesy when approaching a door or a lift. The tradition is that the person on the right should enter the door first, but this can become tricky. Since an Arab expects the person of more importance to go through the door first, he may respect you to move to your left, to let you go though the door first. Therein begins the game of courtesy, because you must appear that you respect him to let him go through first. This often causes delays while smiles are exchanged, as he may believe that you don't understand the concept. He may even consider that as you are a guest in his country that you should go first.
Throwing in a simple "Min Yameen" will alert him to your knowledge of the concept. This means "from the right". Don't be afraid to actually go through first though or it may end up as offense that you don't accept his gesturing! Just don't come across that you know of the concept and expect to go through the door first. That would be considered rude.
The little courtesies sometimes make a difference. This will happen not just only from the Locals but all Arabs, but from the Gulf and otherwise, so it is a little trick to help in gaining those brownie point in the quest to establish a business relationship.
However, this doesn't apply on the roads! On the roads, it is every man for himself, whichever side you are coming from!