The ICAO definition of schedule time is indeed block time, start pushing back to stop on stand.

The movement to use touchdown time is unofficial and seems to be because that is readily forecast on existing systems, and obtainable from the in-flight information (which is obviously key to estimating the arrival time), whereas time taken taxiing etc is not so readily calculable, and is of course dependent on the runway in use.

It is also useful for the increasing number of carriers who announce on the PA "another on time arrival" as they exit the runway, then keep silent as they stop six times on the way to the terminal, and then hold for 10 minutes for a gate to be vacated.