the matrix transforms object-local points/vectors to camera-local.
you can get a sense for what it does by figuring where the (object-local) axes get mapped to. X is (1,0,0), Y is (0,1,0), Z is (0,0,1). append a 1 for points or a 0 for vectors.
the +Z vector gets mapped to…
\begin{pmatrix}
0.95552 & -0.03688 & -0.29262 & -167.536 \\
0.0523 & -0.95524 & 0.29118 & -203.056 \\
-0.29026 & -0.29354 & -0.91082 & 2571.13 \\
0 & 0 & 0 & 1
\end{pmatrix}
\cdot
\begin{pmatrix} 0 \\ 0 \\ 1 \\ 0 \end{pmatrix}
=
\begin{pmatrix}
-0.29262 \\
0.29118 \\
-0.91082 \\
0
\end{pmatrix}
so the +Z vector gets mapped to… the third column.
now, where does a camera-local vector point if that is its value? a little to -X (left), a little to +Y (down), and mostly to -Z, so that’s near. and that is where the face’s +Z vector points, as viewed by the camera.
same for the others.