Earlier quoted context omitted.
Article IV of the Treaty states in part, “No acts or activities taking place while the present Treaty is in force shall constitute a basis for asserting, supporting or denying a claim to territorial sovereignty in Antarctica or create any rights of sovereignty in Antarctica.” https://www.asoc.org/advocacy/antarctic-governance/overview-...
The countries claiming a slice of the pie aren't signatories to that treaty.
Which is to say, most of the people who cared enough to sign the treaty already had existing claims they didn't want repudiated by the treaty (which is why Article IV, in its entirety, also says basically "this doesn't affect any existing claims").