Ignoring for the moment the specifics of video game music, one reason to acquire soundtracks over streaming them is for the control and privacy it enables. Your audio files can be played when there is no expectation of internet access. Additionally, there is no possibility of your listening habits being catalogued and used in ways that you might not like (or even know about).

Back to the context of video game music, for the longest time it was actually difficult to find anywhere that would even sell video game soundtracks. Places like Bandcamp have since alleviated the problem, but I can speak from personal experience that long ago one used to have to hunt for downloads, often without care as to who was providing the DL. This kind of experience can leave a lasting impression that game OSTs are something worth holding onto as local files.