The hooks API literally "hooks" into React's lifecycle, by allowing the ability to save state and force re-renders as needed. In addition, React-Table explicitly implements support for doing rendering of whatever React "cell" components you have supplied as part of the column definition.
Yes, a lot of the logic probably could be extracted as a pure vanilla JS lib, but there'd also be a lot of work that would have to be done to then integrate it into React.
Also, the creator is a fairly prolific author of React-based libraries, and that was his focus when he wrote React-Table. If someone else wants to try to create a vanilla JS version, you're free to do so.