Yes, the fact that they are a Dyad allows him to regain his power, but he already says it without needing that term:
“The life Force of your bond…a Dyad in the Force…a power like life itself.”
it could easily be rewritten as:
“The life Force of your bond…a power like life itself.”
In fact, reviewing that shot, it looks like Palpatine’s mouth doesn’t move correctly to form the words ‘a Dyad in the Force’. It looks like there was something a bit shorter there before, but the Dyad line was added later. Something like:
“The life Force of your bond…incredible…a power like life itself.”
Then just cut the ‘unseen for generations’ line, since it’s said offscreen. I genuinely think that cutting those two instances would streamline the whole plot.