' the system has developed a modern understanding of this term "  In other words we have twisted the real meaning into having it mean anything we want.
1. Self-identification? Is that like if I "feel"  Polynesian, then I am?  Kinda like the transgender folks if they "feel" like a woman today they will use a woman's bathroom.  Or they might "feel" like a man today and use a man's?
2. Continuity of pre-settler society.  NONE HERE.
3. All people have a link to the world around them.
4. All here have the same political system and rights under it.
5. Distinct language, culture, and beliefs. Less than 3% of the people speak Polynesian here, their culture and beliefs are now like the majority of all races in Hawaii, they speak English and practice different customs and religions than they did when first they invaded these islands as settlers.
6. There are no dominant groups here, all equal with equal rights. 

No. No indigenous peoples in Hawaii.