The best Animation Maker alternative to Blender Game Engine is Armory 3D, which is both free and Open Source. If that doesn't work for you, our users have ranked three alternatives to Blender Game Engine, but unfortunately only two of them are Animation Makers.
Armory is an open-source 3D game engine with full Blender integration, turning it into a complete game development tool. The result is a unified workflow from start to finish, making you work faster. No more jumping between different applications.
Verge3D is a powerful and intuitive toolkit that allows Blender, 3ds Max or Maya users to create immersive web-based experiences. Verge3D can be used to build interactive animations, product configurators, engaging presentations of any kind, online stores, explainers, e-learning...
As of today, Verge is most advanced engine with Blender integration. Good BGE alternative.
Compatible with Blender 2.80, better EEVEE support.
Russia
Unlike BGE, Armory has not been discontinued. Armory, like Blender, is also open source, and also just like BGE, you don't have to leave Blender when you make your games.