If I understand your question, let me say the original people who came to the Americas were called Indians for many years, but that is no longer politically correct. We now refer to them (and their descendents) as Native Americans. Correction: I misunderstood the question. "As in" is the same as "in the sense" or "such as in". It's a colloquial expression not much used in writing.

The word "in" is making a reference to the subject discussed in the first half of the sentence. The word Native Americans refers to the fact that they are the indigenous group of people who lived in the area called North America. In fact, the Native Americans too were not originally from the North America region, but rather migrated over hundreds of thousands of years. The word Native American actually refers to a large number of ethnically and culturally different types of people. There were many languages, spiritual practices, methods of finding food. Some cultures existed in large cities, similar to our modern urban cities, while others were a nomad like people. It is important to know that while Native Americans have one name, it is because of their relationship to the Caucasian Europeans who traveled and dominated the present United States. If history unfolded in another way, our world would have a very perception of the indigenous Americans. For now, Native Americans will do.

This isn't old-fashioned or even complicated. They mean "native" like "the first ones here". "As in" = in other words/ for example. There should also be a comma (,) after Americans; that would clear up some of the confusion too. Otherwise your risk having a run on sentence that never ends.

This question states that the sentence "We call them Antive Americans, as in the firsts ones here," uses the word "in". The OP wants to know why the word "in" is used, rather than being omitted.

It is an old fashioned sentence that is why it is written that way.