It doesn’t matter if your daughter has Argentinian citizenship…does she have a parent/grandparent that is 100% Hispanic(perhaps from Argentina)? For example, a Taiwanese and Italian were married and were was living in Argentina that would not make their child Hispanic. But if a Argentinian native person married an Italian, their grandchild would qualify under the National Hispanic Recognition Program.
But if your daughter does not identify as Hispanic, she should not check that box.
For example, my oldest did not identify as Hispanic even those she qualified as NHRP. But my younger one does.