I think a play in browser tag would be very usefull because I find myself waiting for something and hop on to search for some games that I can play quickly without needing to download them. 

I also prefer playing direcltly instead of downloading and deleting a bunch of short games.

You can browse by game type. See in the directory, or the sidebar of the Browse page.

Interesting. Maybe you can give feedback to itch with the feedback button, why you did not notice where those games are.

On the itch landing page, that is hidden to me in plain sight, there is on top left the link to "HTML5 games".

And when you click on browse, there the default view will show you on the left side a menu that is an opened tree with literally "Play in browser" as the very first option.

Curiously enough, those seem to be not quite aliases. It is 408k and 402k games. Maybe the old flash games? They can't be played in modern browsers, but are still on the platform listed as such.

https://itch.io/games/html5

https://itch.io/games/platform-web