Lebensraum. Whether it’s bluster or not, I don’t know. I hope it’s bluster. But it’s straight out of the fascist playbook. It’s like he’s ticking off the bullet points.
The US has made the offer to buy Greenland before - After WW2 when the first treaty that gave them complete military control over Greenland lapsed.
The reason Denmark refused it was partly because Greenland was taking its first steps toward self-determination with the establishment of its first legislative council and because Denmark didn't think the Soviet Union would take too kindly to it putting the US right on to its northern borders!
During the Cold War, a second treaty, Thulesag 2 allowed for the US to take a significant interest in/control of Greenland and gave the US and its troops unrestricted freedom of operation and bases, on land, air and sea, throughout its entire national territory. This included nuclear facilities and the part requiring "respect" for Greenland/Denmark and its citizens was subsequently ignored when the US hoyed-out residents in order to build/expand their facilities, some of which which they had neglected to inform Denmark about.
Then there is a little matter of the US nuclear reactor built under the ice cap to power one of these bases, Camp Century, which must rank amongst the stupidest ideas of the entire Cold War - Reactors get hot and ice moves! Which although eventually removed, left a lot of radioactive waste buried amongst the ice.
Thulesag 2 expired in 2009 in the wake of the Greenlanders massive victory in the referendum on extended autonomy and they required that Denmark took back full responsibility for defence. The US only have one base on Greenland's soil these days and that is a satellite/early warning station operated as part of NATO.
I also have a vague memory that the Danish troops operating in Greenland are the last forces on earth using WW1-era, bolt action Lee Enfield rifles as their primary service weapons. Apparently nothing more modern can reliably operate in the conditions, or reliably take down a Polar Bear or charging Musk Ox..!