WASM probably won't affect most websites today, correct.
WASM probably won't enable cutting edge games. It has been around for years and there's no interest from the gaming community there, the newest additions to WASM like GC won't affect games much. There are other issues with the web platform that prevent this from working, e.g. the implicitly managed disk cache, the relatively old graphics APIs exposed into the sandbox, the performance impact of sandboxing, and a few other things. The games world has Steam and consoles, that seems to be good enough for them.
There might be some attempts to port desktop productivity software to the web using WASM, probably in partnership with Google, like what an architect might use. But probably not. Installing software isn't hard and pro grade software isn't an impulse buy. How much incremental revenue would a web port bring relative to the cost? Probably not much.
700mb programs downloading when a user visits a URL isn't necessarily a problem if that download actually sticks, but see caching issues above. After all, people routinely download programs that large. Chrome itself is ~500mb on disk!