>like it wasn't the extension of a European war...

My comment wasn't intended as a "correction", just adding that historians seem to refer to this war by a different name these days. At least in the textbooks I learned from, it was discussed in the context of the Seven Years War.

The French and Indian war began 2 years before the war in Europe. So in a way it was the other way around (of course there were much more important factors than what was effectively an ongoing proxy war in faraway colonies)