I was watching President Trump's white house daily briefing for Coronavirus and I see officials standing too close to each other which is a different issue. But one thing I am wondering is everyone staring at the president nonstop without looking at the audience? Is there a specific etiquette they are following?
This etiquette doesn't really have a name, but it is "look at the speaker" when someone is giving a speech or talking to a group of people the polite thing to do is to look at them and to give them your attention. If they didn't look at him it could appear like they aren't interested which might make them appear rude. Everyone is noticing the people in the background and they are pretty much part of the audience so if they didn't pay attention it would show that they weren't paying attention which is rude.
When teaching children to pay attention, the phrase "whole body listening" is often used. One aspect of this is to look at the person talking to show that you are giving them your attention.
From a political psychology standpoint...
The people in the photo are the members of the president's cabinet (or their staff). That means they are all either direct reports and/or political subordinates of the president. They all serve at the pleasure of the president. Therefore, there is a certain element of political psychology at play.
Specifically, they all must uphold the appearance being a loyal member of the president's team above all. Therefore, they must show all the outward signs of respect and being a good listener. Visually, this includes focusing their attention on him while he is speaking and maintaining respectful body language. Otherwise, they undermine the president's leadership and their respective security and effectiveness in their cabinet or staff position.