After watching the video he clearly states he is testing the corner case of two wires in parallel to share the current, in which one is smaller in diameter than the other. He is proving the thicker one will fail first which is not the intuitive answer. In summery the thicker wire is passing more current as is expected (lower resistance) but because its ratio of surface area to volume (simplified interaction) is not as high as the smaller wire it is less able to dissipate this heat to the air and therefore gets hotter and melts first. This is a well done test. To give possible context on why this video was shared, in the rare case multiple parallel wires are required due to routing constraints it must be of the same gauge wire. Do not run wires between the same two points in parallel comprised of different gauges. In general all wiring should be a single conductor from one point to another, in which case this test provides no helpful data.
This is NOT a test of given the identical current which one melts first, which is what we are mostly concerned with in van builds (sizing a single wire for the load). In that case the smaller wire will always melt much sooner.