First off, if you bought a Spine Editor license, like Spine Essential, you have no licensing issues. For life 🙂
Spine consists of two parts: the Spine Editor and the Spine Runtimes.
The Spine Editor is the desktop application you use to create your skeletons and animations. The Spine Editor then lets you export your skeleton and animations to various formats. When you want to display your skeletons and animations in a game, the best export options are JSON and Binary. These are export formats that can be read and rendered by the Spine Runtimes.
The Spine Runtimes are code that you integrate with your game to load and renderer skeletons and animations exported to JSON or Binary. GameMaker already includes the code of the Spine Runtimes for you, so you don't have to do anything extra. By loading and rendering your skeletons and animations in GameMaker, you are effectively making use of our Spine Runtimes. There are also Spine Runtimes for other game engines, like Unity or Unreal Engine.
The Spine Runtimes license basically says: you need a Spine Editor license if you use the Spine Runtimes in your games or apps. Since you've bought Spine Essential, you are covered license wise.