The definition of "now" as when the light hits the mirror on each side is a "constructed" now, a false now if you may. It takes the light longer on the right side than the left side because she is moving through space, all that tells me is that there is no way to communicate a "now" between different observers because there can't be instantaneous communication between observers, not that time itself is relative or physical stuff itself doesn't have a constant time?
She says in the video that we have to find a way to operationalize how to find a now, to measure it empirically but maybe that's not possible without running a complete simulation after the fact. But to me it seems not surprising that without instantaneous communication there is no way to create a "now" empirically but that doesn't mean it extends to the ontology of physical stuff itself or time itself. There would still be a time in there (you should be able to see it in a simulation?)
Also for example, if you use sound instead of light, if I'm far away from a sound source (farther than the speed of sound), and another observer is closer to it, we would not be able to use the sound source as a source "now", because I would hear it later. Is this the same type of situation or different? I feel like I must be missing something fundamental here but I'm sort of going out on a limb so please don't slaughter me :P