This map seems to use a very variable and at times generous definition of both “company” and “still in business”.

Sure, Australia Post is one of Australia’s oldest institutions if you count from the date of the establishment of its oldest predecessor (which this map does, as a Postmaster-General was first appointed for New South Wales in 1809), but a single national postal service wasn’t established until Australia itself was established in 1901 and the colonial postal services were merged, and even then it was a government department until 1975, and wasn’t corporatised until 1989 and remains government-owned to this day.