I doubt that MK and the devs who designed the Skyrim Thu'um system collaborated, but the two concepts seem strikingly similar. Given the literal treatment of memories-in-stone, we can assume that the Yokudans literally inscribed knowledge on stones meant to be absorbed rather than read and learned. We see the exact same mechanic work with Dragon walls and knowledge of the Thu'um. The Dovahkiin does not know the Dragon language just like Cyrus does not know Yoku. Miraculously though, once the Dovahkiin absorbs a word, he can speak the language. This is identical to Cyrus not being able to speak Yoku and then absorbing stone-knowledge, learning not only new sword moves but also the language as well as seen here:
“Yoku has forty-eight different versions of honor,” Cyrus said, “And they all trace their roots to ugak-ta, which means, more or less, “I’m pretty mad”. So that might be a yeah.”
Fornower walked by, fetching a saw. “Woke up speaking Yoku, cap?” he said.
“Strange night,” Cyrus said.
Again, I doubt that when Bethesda was developing Skyrim, they based the Thu'um and learning the Dragon language on Sword Meeting, but that doesn't mean the two couldn't still be made to be related within the universe.
In the same fashion it also explains the mechanic behind sword singing. As I've said before in one post, the sword is such a powerful and integral symbol in Redguard culture that things which aren't swords may still be referred to as swords. Therefore if the Redguard have their own kind of Thu'um that allows them to kill people with their minds or voices, as implied by the term "sword singing", they would view that act of violence as a sword action because the word "sword" is synonymous with "fighting" or "violence" or "attack" QED.
In conclusion, the mechanics behind Sword Singing and the more complicated Redguard sword moves, particularly the ones that seem magical can be compared to the mechanics of Thu'um, in that regular sword moves cannot do such things as cause the wielder to become undead, appear in multiple places at once, and split atoms to create nuclear explosions while regular shouting cannot throw people backwards, spit fire and ice, slow time, and deflect arrows. Both forms of fighting could likewise be one in the same, extant on Nirn before magic.