I am also someone who's come to game almost exclusively with something else going on the side. I think it's a cross between two factors: stimulation 'normalization' and more an indictment of videogame music than videogames themselves. The Witness I think starkly demonstrates this as it is, and supposed to be, silent for the atmosphere and thus allows the stimulation aspect to shine through very powerfully. To speak from my personal experience, that last game I can even clearly remember the combat music from is Mass Effect 2, with most games nowadays I find I give the music a brief chance to engage me but then in most cases I realize pretty quickly it's not overwhelming enough, and find something to supplement it.
Which that word, 'overwhelming', leads to part two of my thought: that people doing this have likely become accustomed to such high stimulation that anything lower creates that almost 'silence-phobic' feeling. The volume penetrating our lives has been cranked up and up and up as our media, and especially interactive media, can be with us every step of the day now. In fact a scenario that I think illuminates this is driving, especially commuting: even as the driver (much less as a passenger or on a bus) when on a very familiar route the brain just goes on autopilot (Occasionally with catastrophic results) and barely puts any active thought; even decades before now drivers have sought out music, talk radio, audiobooks, chewing gum, whatever, just craving something that will increase the stimulation level back to more what the person is accustomed to. The point we're at now is just higher up that hill from becoming accustomed to more and more and more stimulation being the norm.