It's got it's own dependency manager, and GOG is one of the pre-configured applications in the Gaming section, so it makes sure that everything needed to run GOG is there. I've never used winetricks/protontricks on their own, but I think the main difference is the sandboxed nature, the devs recommend installing Bottles as a flatpak, and then it makes it's own prefixes within that environment. They also recommend making new bottles for each application, so like if you also wanted EGS or the EA store, you'd make new bottles for each of those rather than keeping them all under one "gaming" profile, for example. Here's docs if you're a reader like me:
I had a friend that had the keyboard controller attachment specifically for this purpose