Do you mean popular in the sense that they'd incorporate existing classical pieces into videogames, as per Tetris, or that they'd push orchestrated versions of existing video game tunes much more into the mainstream than IOTL?
If the former, I've no idea. I guess if Nintendo – for some near-ASB reason – fired all of their composers at the end of the NES era and hired folks to find and sequence public domain tunes in their first-party games without composing original tunes, that'd probably make their consumers a lot more interested in classical music, especially when the SNES came about.
If the latter, Squaresoft (and later Square Enix) could push orchestrations of FF/DQ tunes to classical stations in the early 90s, and they might actually get significant airplay. (Heck, they should've done this with To Zanarkand IOTL, but they didn't.) If they were successful, they would encourage more developers to orchestrate their tunes, and eventually orchestrated game scores could become as ubiquitous on classical radio as film scores.
Otherwise, I can't exactly see video game music becoming mainstream or classical music replacing original compositions in games.