How does this Digital-to-Analog converter work?
Rushing ...

This seems to be how it works from inspection.
 Some fine detail may vary. 

The transmitter sends a series of pulses as shown below - amplitude varies in 4 steps.
 The signal modulates an IR LED such that the amplitude structure is maintained. ie looking at the signal with a linear photo detector at close range would show this signal.



Simple on/off COTS IR receiver ICs are used 


"such as TSOP1138 (Vishay) – 1,52Eur from Farnell or GP1UX511QS (Sharp) – 1,09Eur from Farnel" ( quoting table 8 from here ).


The signal is reflected off a target and returned to the receiver. 

As seen below I have modified the original diagram to make the pulses heights taller. The receiver has finite sensitivity and is either on or off.

At close range (as in 1. below) every received reflected pulse triggers the receiver.The receiver detection threshold is below the height of th eloe=west oulses so every pulse is "seen". 

The RC filter turns the series of pulses into longer pulses. Note on the diagram tha the large fultered pulses are displaced slightly to the right wrt the input pulses due to the time dely in the RC filter. 

At greater range the inverse quare law of signal strength with distnce means that returned amplitude will be lwer. - as shown in 2. below only the largest amplitude ulses are high enough tp trigger the receiver. 

The pulses repeat at the frame rate. The width of the "on" pulse will decrease with increasing distance,