Looks like I'm not the first person to have noticed this about flat screen TVs.
https://www.physicsforums.com/threads/strange-optical-phenomenon-diffraction-or-something-else-solved.867358/ I'd have thought that it was behaving like a CD and being a reflection grating. Perhaps not. I hadn't even thought about the X shape. I have posted before about net curtains giving a + shape diffraction patterns which is due to horizontal and vertical slits in the same material. Does the X relate to the alignment of parts of the screen?