Rockets, especially big ones, create their own artificial, gaseous "wires".
Tall cumulus clouds reaching high enough that their upper parts are ice instead of water droplets generate powerful electric fields. The potential difference ("voltage") between the ground and the clouds can be huge, millions of volts. When the electric field strength, typically measured in volts per meter, reaches the breakdown voltage for air (something of a misnomer; it's actually the breakdown electric field strength), the air molecules ionize, its electrical resistance drops significantly, and a spark ensues. This breakdown voltage is a function of gas composition, temperature, pressure, and even the length of the conduction path! Long paths require lower electric field strengths to initiate a spark.
A cloud's high voltage is placed across the distance to the ground, so the average field strength is the voltage difference divided by the distance to the ground. If somewhere between the cloud and ground the local conditions reach breakdown, the voltage drop across that length of the path decreases significantly (see Ohm's Law). This means that the remaining voltage is applied across a shorter distance, so the field strength increases. Also, at the ends of the breakdown region, the temperature increases, reducing the breakdown field strength, so the breakdown region extends itself—very quickly! Eventually it reaches all the way from the cloud to the ground, sometimes with multiple local breakdowns that merge into one lightning stroke and "branches".
This is what a wire behind a rocket does. Along its length the voltage difference is essentially zero, so the voltage difference from the cloud now is applied to the shorter distance from the top of the wire to the cloud, increasing the electric field strength. This makes it more likely to initiate ("trigger") a local breakdown that cascades into a lightning stroke, connecting to the top of the wire. The YouTube video takes it from there, with exploding wire, etc.
The huge ion trail behind a big rocket acts like a wire. The mobility of the dissociated ions and electrons makes the electrical resistance of ionized gases, even partially ionized gases, far less than for un-ionized gases. The voltage drop across the length of the ion trail will thus decrease, concentrating the cloud-to-ground voltage across the shorter distance from the cloud to the rocket and increasing field strengths. This increases the probability of triggering a local breakdown and subsequent lightning stroke that travels through the rocket and its ion trail.