Ahhh, but this is a totally different concept. What he did was literally(!) turn his breakbarrel airgun into a breakbarrel airgunfirearm!
He used the same principle as used in a diesel engine, hence the process is called dieseling.
That process is to compress a fuel/air mixture to such a high pressure (which makes the temperature of that mixture rise tremendously) so that due to the heat a spontaneous detonation (explosion!) occurs. The added petroleum (jelly) is the fuel part in this mixture used in the airgun.
Now here’s an interesting bit of knowledge:
The similarity between breakbarrel and PCP airguns is that they both use compressed air to propel a projectile, (dûh, they are not called AIRguns for nothing right!

) but the big difference is that the breakbarrel compresses (outside breathing air @ 1 bar, or 29.92 inHg pressure) air by moving the piston in the cylinder, DURiNG the shotcycle. (via the same principle as described for the engine above)
And again because of this compression the pressure increases tremendously and as a result
heat is generated. but since there is NO fuel source (no petroleum jelly), there is no fuel/air mixture, (just air) and thus NO detonation occurs!
Whereas with the PCP airgun,
the air is already compressed beforehand (by use of a compressor, and it is stored in the airtube or bottle of the gun).
During the shotcycle of a PCP there is no heat generated! (Like said: the air was
already pressurised before!)
In fact, quite the opposite happens: due to the release of the air, going FROM hi pressure TO low pressure, heat is EXTRACTED! (You can feel it after shooting a lot with a PCP gun: the barrel feels very cold, and get sometimes damp during those humid days!)
Long story short: the gentleman from your video uses fuel
not for lubrication purposes to increase precision, but to
increase the energy of the projectile being shot. Whereas this topic is about the (supposed) benefit of
increasing precision with lubrication.
Precision is having all the shots land in a
small group (ultimately all in the same hole!),
accuracy is to get them
where you want them to hit (in the bullseye!)