Blender Game Engine is described as 'The Blender Game Engine (BGE) is a component of Blender, a free and open-source 3D production suite, used for making real-time interactive content. The game engine was written from scratch in C++ as a mostly independent component, and includes support for features such as Python' and is a game development tool in the photos & graphics category. There are three alternatives to Blender Game Engine for a variety of platforms, including Mac, Windows, Linux, Blender and Web-based apps. The best Blender Game Engine alternative is Armory 3D, which is both free and Open Source. Other great apps like Blender Game Engine are Verge3D and Blend4Web.
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.
Blend4Web is an Open Source tool for interactive 3D visualization on the Internet. It provides Free and Commercial licenses.
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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.