It looks like that is a dedicated, but otherwise conventional 'Z' axis assembly turned on it's side as part of a simple 2 axis machine built just for this purpose. It's not a cunning add-on to an existing gantry router.

I can't see any mechanism to adjust the drilling height to cope with different thicknesses of board but you could do that easily enough with a set of different thickness shims for the drill mounting if you didn't want to go for automatic adjustment of the bed height. Rather than a high speed router spindle you want a drilling motor. Your old mains powered Black & Decker might do the job

Quite an easy machine to build I would say and could use any standard software such as CamBam, Vcarve or Fusion 360 to generate the G-code for it using the standard drilling machine ops. Just use X (or Y) and Z axes as for a normal router. Plus an AXBB-E and a copy of UCCNC of course.