The difference, for me, is consumption vs production.
If you spend tons of time learning an instrument, you will probably find yourself interesting in creating music. Maybe it's not going to be playing in a band, or recording albums. It might just be playing music around the campfire. But that is an activity in which you are producing something, bringing music into the world. I feel the same about any of "the arts". You're inherently going to be engaged in the act of creating something.
With gaming, consumption is more the rule. You play a level, a campaign, a story. If you create something, bring something new into the world, it is most likely going to be external to the game (like the posters who mention that they built websites and utils for their favorite games).
There are obviously exceptions on both sides. Games like Minecraft, Factorio, etc are obviously creative. Games like Roblox or Mario Maker allow people to create content and put it into the game. Game review videos, Twitch streaming, etc, allow people to build content with games at the center. These are creative/productive pursuits, and I think they have some inherent value (even if it's kind of a bummer that these creations are largely limited to being enjoyed within the game).
As an exception on the musical side, you could, for example, learn guitar exclusively through Rocksmith, and only ever use your guitar as a controller for a game.
I don't think there's anything inherently wrong with using your free time to do "consumptive" stuff. I enjoy gaming here and there. I listen to music. I watch TV. But for me personally, I find that I get a lot more satisfaction out of "creative" activities.
One last point - you get good at what you spend your time doing. I tend to really enjoy games that ask a lot of skill from their players - roguelikes, tight platformers, Souls games, Doom on nightmare mode, etc. But when I finish a game, I no longer have any use for the skills I developed. Whereas skills I develop in the pursuit of something creative/productive can be used in all kinds of situations for the rest of my life.
Edit: I started rambling and forgot the point. With all of this said - I would never want the government to limit how I spend my time. That's a job for parents when you're young, and it's a job for your own sense of what makes you happy when you're an adult. These kinds of lessons aren't things that can be downloaded into you from outside. Realizations about what makes a person fulfilled tend, in my experience, to come from within.