Even if you're writing your own engine from scratch, VR runtimes provide orientation information directly to the engine as a 4x4 transform matrix. They would have to ignore all the documentation and go far out of their way to somehow regress to euler angles, and are likely introducing other precision issues in doing so.
4x4 transform matrices typically represent 3-space transformations with homogeneous coordinates. Rotation matrices in this framework are effectively the same thing as Euler angles. They are not quaternions.
If you want to get pedantic they're also not euler angles, they're 4x4 transformation matrices.
You can pick out euler angles just as easily as calculating the quaternion by taking the basis vectors through the matrix and extracting it from there.
I'm aware of reasons for using a custom engine over Unity or Unreal, my question is what is this firms specific reason for not going that route. Also, Ready at Dawn has been developing that engine for years, and has world class engine programmers that know how to implement headtracking correctly, so the comparison isn't fair in this case.
The best selling/best graphics fidelity (imo) VR game Lone Echo has its own custom game engine.