I’d say your best bet is to probably look at WebRTC for fast communication between two peers. You’ll still need a method to connect the two which means you’ll either need an intermediate server or at least an input field for IP address between the controller and game.
Yep, was why I asked the above question, as It would likely be possible to do something with Hype/App-Script on google. Likely a poll and pull by the web app. But all this really depends on how and who this is being deployed to. Which @jonathan makes valid points