The engine would have to be rewritten from the ground up, including plugs. In a different language.
It's basically the same as asking for a native export.
I read up on the subject a bit.
Seems like WebAssembly (webasm) is meant to allow C/C++ to be compiled to run in a web browser.
Newt, you are correct, it would be like asking for a native exporter level of support. That is why Unity and Godot (and other game engine) are relying on webasm: to have a relatively easy port of their native exporters!
The conclusion is that competing game engines will (probably) offer better performing web games with improved predictability because they have native exporters in the first place which are ported to webasm. Isn't that ironic?
Of course, in practice it will probably not make much of a difference for most games, going by what Ashley says in his article. I do suspect that it may matter for lower spec'd hardware.