There's a "threat simulation theory" that sort of explains it, but it's not 100% correct for everyone. TL;DR: in dreams your brain often seems to practice "threats"/stressful situations. E.g. you're more likely to dream about missing work, having exams, car breaking, running from someone, interacting with someone you care about etc. rather than doing something you're completely used to.
Honestly probably yes to all of those. Except for small children the dreams are probably also non-visual like in the case of blind people. They probably dream about "weird feelings" (chills, shivers, cold, heat etc) and smells and sounds and whatnot. The TST also assumes that some of the instincts are inherited from our ancestors (e.g. that uneasy feeling when you walk alone through the forest at night - because for thousands of years predators could kill you in that exact scenario) so a baby's brain might dream about those feelings too (probably without visuals, just chemically induced feeling of uneasyness).
And back to the screen scenario: To the brain "excitement" is also "stressful" from a chemical PoV. So if you really really enjoyed some game (as a kid or whatnot) you probably dreamt about it too.
I wonder if very small children dream about screens then don't understand. Like, if a poor small child got hit with the car commercial or the maze jump scare, would that get added to the threat list? I'm talking young enough that they can't tell you it's a screen. Do babies dream? What could they ever dream about? Is there a library of set concepts that we're all genetically made to fear, if so, how would that be represented in dreams? Gosh