This is an issue I raised with colleagues back in the late 90's. At the time only high end graphics systems (SGI) had hardware graphics contexts. So one openGL app could crash or scribble all over another openGL applications canvas.
The truth is a GPU is an entire second computer attached via PCIE bus. As far as security is concerned this will continue to be a shit-show until we accept that fact and act accordingly.
This isn't an issue anymore, nowadays there are MMUs which isolate shaders from memory they aren't supposed to touch.
OP's problem stems from the fact that some video buffer used by his browser hasn't been cleared after deallocation. At some later time this buffer either has been erroneously displayed instead of the game's buffer or has been allocated to the game which erroneously displayed it without filling with new content.
The truth is a GPU is an entire second computer attached via PCIE bus. As far as security is concerned this will continue to be a shit-show until we accept that fact and act accordingly.