So basically, MMs are conduits to the trading floor/platform.
However, the order flow would be different for retail vs. institutions or large* investors.
Here's how I picture it:
retail order ---> broker (e-trade, TDA, etc.) ---> MM ---> trade executed
institution ---> MM ---> trade executed
So institutions/large* investors can bypass a traditional/retail broker because institutional MMs are associated with large financial companies that have their own brokerage-type services for large*, monied investors/customers.
*large meaning ultra-rich individuals