The TMZ article OP posted provides a inaccurate representation of the situation. But what would you expect coming from TMZ. The actual restrictions mandated are much lighter. For example, most businesses, stores, and restaurants remain open. All restaurants are open except for the fact that they can only serve take out and drive thru orders. And the grocery stores are open. Much of the service economy, as stated in the article those that provide essential services such as repair, auto-repair, are open. In addition, basically all retail stores, those that " non-grocery products, and products necessary to maintaining the safety, sanitation, and essential operation of residence," are open. This broad definition actually includes "pet supply stores."
Most retailers in fit under this category of stores. Specifically, if a store holds few cleaning supplies, they would be categorized as a supplier of essential goods. And with all these retailers open, the warehouses and delivery services would have to be in operation. How would stores sell if they had nowhere to purchase their inventory. Surely, every business relies on each other in a way. The entire line of business operating on the supply chain would have to be open in order for the retailers to sell goods.
I believe that most citizens won't heed the mandate anyways due to the diversity of the population. So many immigrants that don't speak English as their first language will not be able to interpret the message. And the law enforcement agencies will lack the manpower to carry out punishments towards people who violate the mandate.
The definition on which businesses can/ cannot operate during the lockdown.