This is a facility, in the UK the health centre where it is a private practice of a doctor or group of doctors is often referred to as a 'Surgery', most likely due to its origins in the 'Barber/Surgeons' of some centuries ago.
The Welsh word 'Meddygfa' means simply 'a place where doctors are' from the word 'Meddyg = doctor' similar to Médico in Spanish.
Larger non hospital facilities with a broader range of services are sometimes referred to as Health Centres in English and 'Canolfan Iechyd' in Welsh.
The word for 'surgery' the procedure is 'llawdriniaeth' which is literally 'treatment by hand'
I thought that might be the case, but thought I'd ask more out of curiosity as to the usage.