While I personally would rather not put an extra cycle on an engine by starting, going out to the run up bay then returning and shutting down prior to boarding, there are often valid reasons for this practice. For example, if the aeroplane has to be relocated from hangar or tie down to the terminal, the cycle may as well be used for the run up. Or the runup bay may be in an inconvenient location, or subject to waiting times at peak hours.
As someone points out, there could be a difference between what is required on first flight of day and subsequent short turnarounds. That policy is up to the operator to establish with the regulator. And often will have to reflect what the flight manual stipulates.
Another argument: Just because it works now has no bearing on how it will work in five minutes time (e.g. testing landing lights achieves nothing except to shorten the life, as like so many devices, they usually have a finite number of cycles between failure).
If a piston engine is running smoothly and makes power during the intial take off roll, there is no reason to suspect problems.
Some operators may also call for a mag check and fire test prior to the last shutdown.