Yes that is absolutely a valid way of approaching the problem although you do then sometimes run into the problem that the game you’re trying to play is no longer supported (service been shut down left and right).

I also think it’s a bit unnecessary, by all means play the classics if that’s what you’re into, but if you’re doing it to save money, it’s not as if there aren’t high quality indie games being made right now, so it’s not like you have to just play old games to be frugal.