For licensing reasons, I think the approach Armory3d is taking, with a fully external permissive licensed (zlib) engine, is the only viable route.
As far as I know, EEVEE code is part of blender and under the GPL. This makes it unviable for practical use in a game engine that supports closed-source games… because any non-trivial game will require you to write native code, and GPL says that code would need to be open-sourced.
If they make a new EEVEE BGE under the GPL, it will be just as irrelevant as the old BGE under the GPL. A few indie and open-source people can make game prototypes, but no actual games will be made with it.
Also … “EEVEE is a renderer, not a Game Engine.” Therefore, the OP’s question actually does not make any sense at all. “Apples and Oranges.”
EEVEE was intended to gift Blender with an engine that takes advantage of the graphics hardware that is now universally available in today’s computers – capabilities which did not exist when “Blender Internal” was architected. Furthermore, it uses that hardware in the way that its designers intended, vs. Cycles, which uses it as a mathematical array-coprocessor. (AFAIK, “the jury is still out” as to whether Blender Internal will survive, but that discussion is not relevant here.)
The render-engine implemented in Armory is separate and distinct from any of those which are available in Blender, but for obvious reasons it most-resembles EEVEE.
They mean a game-engine based on the EEVEE PBR GPU rasterizer.
While EEVEE has some multi-stage non-realtime techniques, it’s rendering and shading is pretty similar to what is done in UE4, Unity, or Armory3d. It’s a deferred dynamic lighting based PBR rasterizer, with tricks like Shadow Mapping, Environment Mapping, Screen Space Reflections, and SSAO.
The ways some of these “fake light path” techniques are handled in EEVEE vs UE4 become even more similar if/when everyone starts using NVidia RTX real time hybrid ray-tracing.
If something like the old integrated BGE logic and physics were mixed with the EEVEE renderer, the visual results would be similar to UE4. (though not necessarily as fast)
As I said before, I don’t forsee this happening, because EEVEE is GPL and there just isn’t much value to a game-engine constrained by the GPL’s restrictions. Even the LGPL’s re-linking requirements create issues for non-open-source mobile apps. It would need to be under a more permissive license (MPL2 or artistic), and that is pretty unlikely to happen.
I believe and hope Blender will stay focused on their goal of creating an “interactive” mode within blender, used for creating content (maybe like source filmmaker) or for interactive editable blend scenes… but not for packages games.