Check ICAO annex 11, section 3.7.3.1.2. It states "The controller shall listen to the read back to ascertain that the clearance or instruction has been correctly acknowledged by the flight crew and shall take immediate action to correct any discrepancies revealed by the read-back."
Pretty clear.
You assume they are all on the same frequency. The recording clearly states that it is a combination of several frequencies. Does anyone know for sure who was on which frequency? If so, please enlighten us with concrete proof. Otherwise, it looks like the controller missed the read back and that contributed to this 14km "close call."