Hi there,
Understood the requirements and watched your video. I could build this for you. For the testing purpose I'd use my own test FB app, but you will need a FB app with correct permissions (I think we'd need email and user_friends).
Would use bootstrap to make it nice and responsive, clean PHP and JavaScript. I was thinking, it would be also possible creating a tool where you could generate new games automatically, but that would be a bit more expensive. For now we can go with manually built games which I'd make for you 1 by 1 per price we agree.
My bis includes the base app and a single game and making all that functional. Base app would be the header, list of games, allowing user to play a game and the final image generator + popup to share the resulting image.
Later we can add more games and other widgets like on the sample site, or any features you'd like.
Regards,
Julijan