Can I integrate the game to my site without using iFrame?

I need to integrate the game without an iFrame, because I would like to change my site appearance when certain games event occurred.

Maybe if I prepare a canvas with a certain size and inject the game to the canvas, but I do not know how to achieve it. Or maybe there's another alternative that construct 3 supported?

Thanks

I would like to change my site appearance when certain games event occurred.

You can do that even if the game is in an iframe. JavaScript APIs like postMessage() let you send messages between the iframe and its parent frame.