What is a "21cm/mm absorption system" in the context of measuring old photons from quasars?
They have both 21cm and mm-wave observations for those systems.

Caption to Fig.1


  The hollow squares correspond to two 21 cm and molecular absorption systems.


By "system" they are referring to sets of absorption features caused by multiple clouds of material along the line of sight to a single quasar. Each cloud imposes its own set of absorption features. The totality of these absorption features is referred to as a system.