Looking at the rest of the report, I would say it was simply down to incompetence (and that is being kind).
As you pointed out, there is no record of the flow rate they supposedly recorded. And you are right that if the inlet temperature was measured at a throttle point, then the venturi effect would reduce the temperature seen by the thermocouple.
Of course there is no record of the power taken by the airpump, which is all part of the system - as the unit would not work without it. As mentioned above, measuring the inlet air temperature does not allow them to ignore the pump power.
Another glaring error is in not carrying out a measured run without the arc - just with the air flowing. This would have at least shown the temperature distribution caused by the airflow itself.
Allied to the above is the issue of exit thermocouple placement. As mentioned earlier in this thread, the "vortex tube" has a natural propensity to create a radial gradation across the exit. Ideally there should have been a long diffuser between the unit and the temperature sensors - so that the exit air could mix properly. Placing thermocouples at the immediate exit, as they have done, will subject them to massive inaccuracies, depending on their position in the flow (i.e. the edge will be hot, and the centre will be cold - just from the cyclone/vortex effect).
Bizarrely, there is even a section in the report which acknowledges that very point:
That quoted section above, on its own, completely invalidates the entire report.
The measurement of the electrical power going to the arc is another issue, but it isn't even worth going into that.