Mozilla started work on just such a game engine some time ago and it has just reached version 0.1. It is still at the early prototype stage, but it is usable – as long as you are prepared to find out how it works by reading the code. There is an introductory tutorial, but it isn’t well explained and it runs out very quickly.
The new release includes an entity/component style framework for game resources and the rendering is performed by the CubicVR library. The good news is that the Mozilla team isn’t trying to reinvent the wheel – it is reusing existing code to get the engine up and running quickly.
At the moment there is no 3D physic engine, but box2D is incorporated for 2D physics. There is also a new standalone math library.
As a sanity check a demo 3D game is being developed at the same time as the engine based on the No Comply WebGL demo.
If you want to get involved in trying out Gladius, your main task will be to find your way though the undocumented code. As with many an open source project, the documentation lags behind the code. In this case there isn’t currently even a listing of objects included in the API. Fortunately the code is written in an excellent style and this makes it easier to read, but even a fragment of documentation might create some enthusiasm in prospective users. My advice is to look at the CubicVR documentation for clues as to how Gladius works.