Yes. Some will only allow open driving with a full Irish licence, sometimes it's a full EU licence. In the case of tractors it is a valid licence for the vehicle (ie a 16 year old with a tractor licence can drive). The definition is usually too long to fit on the cert. Therefore it usually will have some reference (any driver aged 25 to 70 with a licence as defined etc etc). All companies have different variations and specifications for their open driving.
*I am assuming that the OPs dad had open driving on his car though it hasn't really been specified*