There's several web APIs for browser window positioning, like screenX/Y[0] (which is what OP uses), which allows for those classic pop-up based browser games from over a decade ago, like Browser Ball.[1]

[0]: demo: https://mdn.github.io/dom-examples/screenleft-screentop/

[1]: https://romanbaiocco.github.io/browser-ball-reloaded/

Actually, they do, sort of. At least, if you use GLSL shaders. I remember some demo project using it in a way that made it appear that the website "sees" another window with the same website, which blew my mind when I saw it first. Cannot recall the name or anything else to locate it.

Wait until they realize that on mobile they can use accelerometer data to keep the element in the same position in space across translations of the device.