Is high temperatures breaking the circuit?
No the effect breaking the arc is definitely not related to the resistance of the metallic material.

If you watch closely you may notice that the shape of the arc does not maintain a straight line between the contacts. An arc basically consists of ionised gas. That's why it is conductive. And it's ionised, because it is hot. But hot gasses are of lower density than the surrounding cold gasses and get buoyant, i.e. they tend to rise. So the shape of the arc gets deformed until it is long enough to die off.

So when does it break? Any power source connected via conductors to an arc can deliver a limited amount of current to it. And as the arc has relatively low resistance the current is clearly defined by the voltage of the power source and the resistances of the source and connected conductors. 

After the arc is built up it tends to elongate, as the plasma is migrating upwards. This increases the run length and because even a good plasma is not as superconductor, the resistance increases. This leads to an increased voltage drop which in turn decreases the current supplied by the source over the conductors. 

At some point in time, the current has dropped so much, that the plasma is not heated sufficiently any longer. The resistance will rise suddenly. It will quench and fall apart. This is when the arc breaks.

Arc welding cannot be compared with this, because the power sources for arc welding are designed to deliver a current just enough to hold a very short arc for a longer period. Those short arcs are so small they cannot extend and change their run length significantly. Perhaps the heating of the material can in fact play a role there. While in the video you linked, it doesn't.

There are plenty other videos on YT showing that effect in greater detail.