I think a more honest comparison (in theory) would be to compare a site used to serve music with spotify. For those that use spotify a link that opens up spotify is probably vastly superior to anything a site can do, that's not to say that the site itself doesn't have any value. But the act of playing music is something spotify better at - and that mainly is just because (if you use spotify) you have your music collection in one place. That's where you go to play music.
Playing a game locally doesn't have to be more than pressing an hyperlink. Steam is probably the, currently, best place for this but, I know, relying on something such as spotify, steam or flash sucks. But there is nothing to say that we can't have an open android/iOS-market-like place for doing this. Apple and Microsoft will push their own markets and I'm surprised that the notion of a third party market hasn't come any longer than steam. I guess people are just too greedy.
There really shouldn't be any reason for why running it in the browser should be any better than running it locally. Have sandboxing as an option (or requirement), similar to what apple does, and go nuts.
I miss the days when running low-level code in an all-purpose browser was something that was considered moronic.