
The term indigenous is usually relevant to contrast to a second colonizing group. Given that Argentina attempted to force the Falklanders to switch to Spanish during the occupation, I would consider that colonization. Hence the British Falklanders are an indigenous people subject to Argentine colonial aggression.
The Argentine pseudohistory about the Falklands is crazy btw. They try to present the revolt of ranchers against the guy Argentina put in charge as being a revolt against British colonialism. They also claim the British expelled all the argentines from the islands. They did not. The Argentine ranchers just integrated with the British shepherds.