It's very much a game server, you are correct. It is also someone's livelihood.
For Garnet, paying the host for the game, web, and databases on bare metal servers have a reoccurring cost. For the host, they have to power and store those bare metal servers somewhere, a reoccurring cost. And so it continues.
PayPal offers a way to cancel these reoccurring purchases. A way that is fairly easy without hassle. They process the payments, they provide a way to cancel them. YouTube(Google) is large enough to work/process payments directly with banks. They have teams of people dedicated to processing and canceling payments.
While I don't like the concept of reoccurring monthly subscriptions as a whole, that's how it is. Once the big players start doing it, it trickles down.