Yeah I think the light use of the word genocide doesn't make justice for the instance where there was actual genocide, which is when you murder people with the explicit intent of destroying a nation/culture/group.
The approach of colonizers from the west in the new world was broadly genocidal though. Like, "we want to live here, so go on git." Killing buffalo to literally starve natives, for example. Allowing natives in occupied lands to be only slaves or dead, for example. Even if it doesn't 100% fit whatever hard definition you're using, it approximates it pretty goddamn well.
