They don't use an irregular z-buffer. They don't even need a Z-buffer. Pay attention again: instead of storing depth at each pixel, they store the triangle's plane equation coefficients. A Z-buffer is used to store depth. If they don't store depth, they are not using a Z-buffer.
Also the how does the irregular z-buffer fit into this?
The picture is a visual description of "depthAtReceiver >= calculateDepthAt( planeEquationCoefficients, x, y );"
So where does this https://developer.nvidia.com/sites/default/files/akamai/gameworks/Frustum_Trace.jpg fit into what you just described.