Young adults were always the ones pouring the most money in the industry. Kids may have been more numerous, but they/their parents spent less. A good example of this is looking up old usenets posts, the majority of which were written by university students, and see how some of them owed literally every console out there and tons of games for them.

Sony knew this, and considering that Nintendo had already cornered the "kids" market, it only made sense for the early PlayStation marketing strategy to be aimed at young adults. Of course this changed after a couple of years and they started including everyone, but at the start yes, it made sense