Flight Instructor landing at a non-towered airport reported they observed an aircraft on short final from the opposite direction and expedited their taxi off the runway.

Narrative

I was conducting a training flight with a student into ZZZ. Winds were 200 at 6 and we were approaching to land Runway XX. Position calls were made at 10 miles; 5 miles; 3 miles; 1 mile; short final; and landing rollout; all including runway number. On short final I observed a target on ADSB that was approaching Runway XY at approximately our indicated altitude and descending. At no point were any radio calls ever made by the opposite aircraft. Upon landing I made visual id with a Piper Seneca approaching to land in the opposite direction. I added power in an effort to make the first taxiway exit and upon turning heard the Seneca make a radio call that they were going around and a second call approximately three minutes later that they were lining up to join the final approach fro Runway XX. At no point through the process did they ever make any other radio calls. Later on I was informed by a third party that a passenger in the Seneca had been hearing my radio calls and finally informed the pilot that they needed to go around.