Didn’t see the video, but I’m not a fan of western dressage,
Yes, dressage just means training, but western has their own training programs for any upper discipline , that also puts body control on horses, but with a different frame and with self carriage (loose indirect rein )
I guess it allows people to ride 'dressage in a western saddle, but to me it makes about as much sense as to have English reining in an English saddle!
It is also more suited for those western breeds that have a more upright neck and head carriage and use way more contact on the reins from stock horses
IE Morgans and Arabians