Does a prior offence for the purpose of calculating a minimum disqualification, or whether the court has a discretion not to interfere with a person's driver's license, include a previous traffic infringement notice (TIN) for drink driving?

Yes.  See the Supreme Court case of DPP v Croaker [2001] VSC 342.  In that case the Magistrate hearing the case treated the offence (the subject of the hearing), as a first offence, on the basis that an earlier traffic infringement notice did not result in the recording of a conviction by a Court.  The DPP appealed this decision, and on appeal the Court ruled in favour of the DPP holding that a TIN did amount to a prior offence for the purpose of determining minimum disqualification period.  The Court characterised the TIN as a statutory finding of guilt once the 28 day period (for objection to the TIN) had expired.