That video is about how "self-similar" is not sufficient for fractal. (The rest of the requirement is some notion of fine detail at every scale, which the video focuses on.)
It is widely agreed that self-similarity is required for fractal, although often interpreted as quasi/statistical/multiple similarity
Put another way, some things are self-similar but lack detail (for example, a straight line), and some things have detail but not similar detail at all scales (for example, a meterstick with ticks at every millimeter) and some things have infinite detail but no similarity (for example, purely entropic noise that cannot be compressed or expressed as a structure)
The core idea of a fractal is something having fractional dimension. It just happens that the ones we know of are self-similar. If we had a formula that generated different shapes ad infinitum, I would also call that a fractal.
It is widely agreed that self-similarity is required for fractal, although often interpreted as quasi/statistical/multiple similarity
https://en.wikipedia.org/wiki/Fractal
Put another way, some things are self-similar but lack detail (for example, a straight line), and some things have detail but not similar detail at all scales (for example, a meterstick with ticks at every millimeter) and some things have infinite detail but no similarity (for example, purely entropic noise that cannot be compressed or expressed as a structure)