We use the coffee brewer to boil water and discharge it after manufacturing and outgoing QA testing process. Is the discharged water considered industrial wastewater and needs to be processed through the Wastewater Treatment Plant before discharging it?

The requirement for treatment of wastewater depends on the quality of wastewater generated from a process.
It's recommended that the facility should get the wastewater tested and after comparing it with the legally allowed parameters, should decide if the wastewater is required to be treated before the discharge.
In all the countries, the legally allowed discharge parameters are defined by the respective pollution control authority.