What this experiment does is very similar to how an ordinary LIDAR unit operates, except that during a LIDAR scan the laser and the receiver are always pointed in the same direction, while in this demonstration the detector is scanning the room while the laser is stationary and is firing across the room.

But in principle, a LIDAR could be reconfigured for the purposes of such demonstration.

If one wants to build the circuit from scratch, then specifically for such applications there exist very inexpensive time-to-digital converter chips. For example, Texas Instruments TDC7200 costs just a few dollars and has time uncertainty of some tens of picoseconds.