Lutris support browser games, but it launch external web browser. In my opinion, it’s not good in UX. Better implement minimal web browser. Mozilla offers Prism many years ago and I liked this idea.
This browser could be designed to play games, like hide navigation buttons and url bar (it could been viewed by click on special button or button on keyboard), offers controls to switch to fullscreen, allows to install Android version from Google Play Store on associated mobiles, etc.