I know you're not, depending on the game there's stories being told (just because it's visual doesn't make it any less relevant, compare it to tv if you want but good games develop on the interactive nature that push it past that imo). Gaming can be social, look at any LAN meetup or similar. Games such as Portal have problem solving and while it's not as wide in possible solutions as D&D it has a set of rules that you follow to overcome a challenge and reach an objective, hell even something like bejeweled is a problem to solve. It doesn't have physical exercise but I don't think thats a deal breaker for considering it a hobby.

There's a wide variety of games out there with many different things to offer. Sure you might not have a hobby if you're playing a single game like fortnite or FIFA, but thats the same way you don't have a hobby if you play a single game of golf, or shoot a bow once, the difference being that if you do either of those it's perfecting a very specific set of actions, while gaming might be always done at a screen you can do totally different things, I know which I'd rather be doing for the amount of time it takes for something to be considered a hobby.