Hello.
Thank you for asking.
Im using it without airgap.
I believe that air gap is just to avoid core saturation and / or reduce the inductance
i tested the same setup with a toroidal ferrite core with outer diameter of 28mm from car audio amp, with the same windings as on the tv flyback core,
It worked better, but was a b*tch to wind!

I dont believe at all that Stan's transformers was Flyback topology, but LLC transformer (resonant transformer, that ones that uses separated coil formers, instead of one over another).
See on google: LLC resonant transformer.