The reactivity system in react is certainly "outdated" when compared to Vue, Svelte, Solid, or pretty much any newer framework. But it's just as you said, the larger ecosystem does have its benefits. There are a few libraries like Framer motion, that don't have equivalent support in other frameworks.
I was clicking so fast that I lost count of whether my previous click was the first or the second card flipped. I think it would play better if you only needed to get two consecutive ones right, rather than resetting after two guesses.