The pitot tube here does not do anything special- it's simply a pitot tube, static port, and venturi all combined in one instrument. It delivers these three pressures to the pressure instruments from three separate ports. The part that plugs into the aircraft looks something like this:
From there, the pressures can be used to drive a normal airspeed indicator, total energy compensated variometer, or any other pressure instruments.
The excellent answer here describes how a backwards-facing pitot probe can be used to make a total energy measurement. Facing a pitot tube backwards negates the value of the measured pressure- it turns $\frac{1}{2}\rho v^2$ into $-\frac{1}{2}\rho v^2$, i.e. a suction. It just so happens that a venturi tube also creates a suction proportional to $\rho v^2$, so a venturi tube can be used in lieu of a backwards facing pitot tube to accomplish the same measurement.
Specifically, the pressure in drop in a venturi tube is given by $ P_s-P_v=\frac{\rho}{2}(v_2^2-v_1^2) $, where $v_1$ is the true airspeed and $v_2$ is the speed of the air in the venturi tube. $P_s$ is the pressure at the opening (i.e. the static pressure) and $P_v$ is the pressure as measured by the venturi tube.
Assuming incompressible flow (which is a good approximation for so long as the flow is sufficiently subsonic), $A_2v_2=A_1v_1$, where $A_1$ and $A_2$ denote the cross-sectional areas of the mouth of the venturi and its narrowest point, respectively.
Putting this together, the venturi pressure is given by:
$$ P_v = P_s - \frac{\rho v_1^2}{2}\left(\frac{A_1^2}{A_2^2}-1\right) $$
If $A_1/A_2$ is chosen to be $\sqrt2$, this equation is identical to the one in the linked answer, and so works identically to a backwards-facing pitot tube in measuring total energy.
