There's a 2nd big assumption:
That tidal energy extracted is additional Earth's rotational energy loss above what Earth does by itself.
According to the paper, tidal energy is dissipated through friction between ocean water & the seafloor. This dissipated energy subtracts from Earth's rotational energy. And some rotational energy is transferred to the moon (which makes the moon move further out). Ok so far.
Author's 2nd assumption is that as tidal energy is tapped, this is extra energy that subtracts from Earth's rotation.
But is it? It might also be that tidal energy extracted by humans, comes out of some fixed 'budget', and the remainder is dissipated naturally. More tidal energy extracted by humans -> less tidal energy dissipated through ocean vs. seafloor friction.
Kind of like solar influx: it's a huge but (apart from fluctuations) fixed amount. We can tap some % of that potential, but what's available doesn't increase. And what humans don't tap, gets absorbed / radiated out by other natural processes.
I won't even hazard a guess. But it would be interesting to figure out which of those applies.