Parallel rendering of an HTML page means an improvement of one renderer to 2 or more renderers. Writing a web server means possibly handling thousands to millions of concurrent requests, which isn't really doable with Rusts 1:1 threading model.
But the reality of concurrency and hardware is that all we have at the end of the day are threads anyway. So in Rust you could have a thread running an event-loop that serves your web sockets. People are building these sorts of abstractions for Rust but they are a work in progress as far as I know. MIO[0] is one such example.
Rust is a programming language for systems programming and "server side programming" is just a subset of systems programming.