Game controller through website?

I would like to make a game with a controller system similar to the one used in the game Jackbox Party Pack.

(I'm using VRChris' explanation for the Jackbox Party Pack)
In Jackbox Party Pack the game is run on a device such as a PC or console. The game displays a website and room code on the screen. Players connect to the game using their mobile phones or tablets by navigating to the displayed website via their web browsers and entering the room code into the site. Once all players have...

Game controller through website?