If you pick a standard interface for your WASM IF (rather than every game having its own ad hoc JavaScript), you could survive the death of the browser by reimplementing the WASM spec and hooking it up to whatever inputs and outputs your interface specifies.
If I were building a new IF system today, I’d use WASM as the VM and build a DSL that compiles to it and a web-based front end that interacts with the WASM code through a standardised API.