I will give a lecture about Haskell next week and might use this website for demonstration.

For one, it demonstrates how far the ghc wasm backend has come, in that such a large system as ghc itself can now run in wasm

yeah why would anyone want to run code on a website

I think the immediate and obvious case would be educational materials. Other than that, technical achievements need not always be practical to be cool :)

In addition to the other responses, it's also worth noting that wasm itself is useful outside of the web itself; e.g. in containerized applications.

Compilers are complicated. WASM has been a priority for the Haskell community for a while. Demonstrating GHC's ability to compile itself to WASM is thus a show that it is robust enough to compile a very complicated program into this backen.d

Have you ever used Godbolt? The Rust playground? The Typescript's playground? The Go playground?

It lets you have that without the pain of hosting compilers server side.

Teaching