So, let me know if i get this right...
Any airline that operates charter plane services to the government isn't a commercial entity?
Any freight company that ships equipment for the government isn't a commercial entity?
Any paper company that sells supplies to the government isn't a commercial entity?
You are missing the main difference between the contract SpaceX is operating under compared to Boeing, Lockheed, etc.
SLS is a fully funded government rocket whose design, construction and operation is at all points along the way approved by NASA oversight.
Orion is a fully funded government capsule whose design, construction and operation is at all points along the way approved by NASA oversight.
Falcon 9 was developed by SpaceX, on its own dime with no NASA oversight or approval needed. They have contracts already in place to launch commercial satellites and payloads.
Dragon has been MOSTLY developed and funded by SpaceX. They got awarded a contract for 1.6 billion to make 12 deliveries to the ISS. As part of that contract, they were given 300 million to both finish development of the capsule and pay for the Demo launches. Mainly due to the fact no independent company has ever sent anything to the ISS. It cost upwards of 100 billion to put in orbit, so they don't want any random company smashing into it.
This method of contracting SERVICES to the government, as opposed to the R&D, PRODUCTION and MAINTENANCE that current contractors do it is new.
SpaceX is operating under fixed price contracts to provide a service to the government. The same way FedEx does. The same way Overnight Shipping does. They assume the risk. That is why its commercial.