To me, the key is to meditate for a few minutes before each decade on the upcoming mystery.
It's the meditation that makes the Holy Rosary fruitful. That's why Our Lady requested meditation as part of the First Saturday devotion. If it becomes an exercise in a repetitive rattling off of words, then it bears no fruit and does become boring.
So, on a related note to what he's saying. to me, meditation on either a mystery of the Rosary or a Station of the Cross is not a meditation of the externals. I try to meditate about what's in Our Lord's or Our Lady's heart and mind when it's happening, their love for us. So, for instance, we can think of the physical pain involved in the scourging of Our Lord, and imagine the physical damage, but if instead we focused on how much He loves us while He's enduring that, what He's thinking and experiencing internally, it beomes a completely different meditation, and you achieve that "connection" that this Friar in the video is discussing.