At least the author is aware that the costs and difficulties of extracting oil in and around Antarctica outwheigh the benefits for now. This is an advance on some of the wild eyed nonsense that has been written about the continent to date.
However, it remains difficult to be concerned. Although oil prices may rise there are plenty of other sources - pre-salt layer oil, unconventional oil in Canada and South America - that can be expanded before we go looking for the stuff in antarctica. After all, there are no identified fields in the region and, despite the author's attempts to whip up concern, exploration to date has been trivial compared to other regions.
There are other issues claiming out attention.

Or we could wean our dependency off oil by investing in renewable energy sources, just a thought...

Looking at Antarctica from this time it is hard to see what the
conditions in the rest of the world would be like at a time when the
price of oil made exploration and drilling in Antarctica economically
feasible.

There may longer be the infrastructure available to produce the
physical material and the support infrastructure to mount such a
exploration, & drilling enterprise.

The oil might as well be on Mars than Antarctica.
Although by the time that the politicians discover that they have to
go to Canberra by train, then they might acknowledge the problem and
fund exploration in Antarctica

Very interesting article, so many issues to consider. I think any starting point as you mentioned is the fact that the ATS is only recognised by Australia, New Zealand, Norway, France, Chile, and Argentina (since 1959, f...reezing all territorial claims). It has been an amazingly resilient international Treaty, one of the most successful there is, but we are in the domain of international law here, precarious to say the least, especially where major States like the US or China are not a party. In saying that, the environmental focus of the ATS has become the prime international justification for the Antarctic regime and probably has the most chance of success by maintaining this approach. Any attempt at asserting sovereign claims for resource related purposes by any of the claiminat states could lead to a very quick collapse. I wonder how effective any such amendments might be.
The issue of whaling is also an interesting one in the context of Australia's territorial rights within the AAT.

You really do have to wonder just exactly how determined we are to destroy the planet at all costs. After the recent oil spill in the Gulf how could we even consider destroying the Antarctic. There is no guarantee that can be given that could eliminate the chance of a repeat of the numerous oil spill disasters we have suffered over the years.
Severin put it nicely,
"Or we could wean our dependency off oil by investing in renewable energy sources, just a thought..."
Will we ever bite the bullet and face up to the hard yards that we need to do to improve the way we treat the life support unit we call Earth before it rejects us?

Nairbe;
Hunger is a strong driver. If falling oil supplies causes a large fall
in food production and significant rise in food prices, many people
in the world will go hungry and maybe starve.

Could you say to them, well there is some oil down there but we will
leave it there. I know, I know, renewables, but next to impossible to
apply to farming.

A transition will have to be made but no one was listening 20 years
ago when we should have started the transition.
Now anything that will slow the depletion will be grabbed with both hands.