React is a library for building user interfaces on websites.
The core idea is to "rerender" the entire UI every time something changes instead of modifying only the element that changed.
In games that is usually done anyway. In regular intervals e.g. 60 times per second the entire screen content in a game is rerendered.
Doing the same thing on a websites used to be considered too slow, so programmers avoided it and instead only changed what needed to change.
The problem was that this complicated web design since rerendering everything is simpler and makes the code more modular and easier to maintain.
So React offered a way to solve this by making the rerender approach much faster. It achieves that by pretending to rerender everything while in reality the library determines internally which components actually need to be changed and only changes those. But that process is transparent and the programmer doesn't have to worry about it.
So the difference between a reactive web site and most games is that the game will actually rerender everything for real while the React library only behaves as if it does so.
Now we could ask why browser manufacturers can't simply make the rendering process of graphical elements faster. But that seems to be tricky for some reason.
I found a post on ycombinator about that question.
https://news.ycombinator.com/item?id=9155564