Why does electric arc in a switch prefer a curved path over a straight path?
There are two combined phenomena:


The current chooses always the least resistive path, that is not necessarily the shortest, as can easily be proven by physical circuits;
Such high voltages and currents have an ionization effect on the surrounding air (electrons are stripped off of the atoms) that cause it to become more conductive in the area where this current is flowing, but at the same time also hotter; this hot air is lighter than the surrounding colder air so it starts going upwards, but still leaving this "conductive" path in which the current continues to flow.


This process ends when the path of more conductive air becomes too resistive for enough current flowing in it, and the ionized air goes up, replaced by "normal" and less conductive air, which is not conductive enough to create the arc. Probably the arc was caused by an event, such an overvoltage, or simply, as in one of the videos, an object that lowered the resistance between the two contacts; OR, like the video in the example, a switch that is opening. When the arc fades, it's also because this triggering event has ceased.