(Firebase founder here) I used to work for an RTOS company, so I do understand where you are coming from. Real-time has different meanings in different contexts though. For an operating system it means hard guarantees on response times.

Over a public network this is impossible, so it instead means that data is being pushed to clients as quickly as possible. The "soft real-time" phrasing might be accurate, but it is a distinction that is probably not helpful, as I think it would confuse more people than it would help, and people in the RTOS world know the difference anyways.