You can't really talk about metric modulation without discussing Elliot Carter, a master metric modulator (say that three times fast!)
I agree that the passage discussed in the clip is a hemiola, but not for the discussed reasons. Much like a tonal modulation, metric modulations are only considered so if you stay where you're going. For example, if John Winter turned those half-note triplet hemiola into dotted quarter-note pulse, and stayed in 6/8 for the rest of the section, then yes, you could identify that as a metric modulation.
However, the question was not whether or not the clip contained a metric modulation, but how to notate one.
View this excerpt from an Elliot Carter piece:
Looking at the modulation from 7/8 to 2/4, you see very clear notation. Carter shows the unit beat subdivision equivalency and qualifies it with a tempo marking (bpm). To be absolutely clear, he also used arrows to indicate that the quarter tied to dotted-eighth only belongs to the 7/8 measure while the quarter note only belongs to the 2/4 measure. This method is the clearest way to notate metric modulations.
This method is also discussed in two of the most prominent books on music notation: Kurt Stone's Music Notation in the 20th Century as well as Elaine Gould's Behind Bars.