I don’t mean this to attack anyone that commented. Seems like I’ve sparked a good discussion. As an instance admin I can see who has voted on posts and literally no one voting on my comment left a reply :-)
When the early European colonizers arrived in the Americas (Christopher Columbus and those who followed), they thought they had circumnavigated the globe and arrived in the lands east of India (which were referred to as East Indies at the time).
So, that's why they referred to the indigenous people of the Americas as "Indians" and the name stuck.
Yeah, even the actual sentiment of the video is more like, "it's not great but it's the name that stuck and there's solidarity behind it."
The problem, as always, is lumping people together when they didn't ask to be. Most of the newer, more "politically correct" terms are even more generic and alienating, and, once again, being forced on them from outside.
It's a person by person thing and I suspect age plays a large part in feelings towards the term. In general I would say avoid the term unless it is requested.