Given the Northern Lights are visible in the video, I think it's safe to assume it's the Great Circle route.

I'm curious: how is it possible that the lower-latitude route is almost one thousand miles longer than the great-circle one, and still, one plane took just 11 minutes more to get to Paris than the other at almost exactly the same speed? Or maybe I'm miscalculating and the extra 2 knots of average speed make that much difference in 7000+ miles trip.

What other factors not shown by FlightAware should be taken into account in this case?

It would be great if there was an alternative visualization with a polar view or at least a projection where the cylinder is angled so the midpoint of the flight touches the cylinder. Long east-west flights are much easier to understand that way.

True but from the video it's obvious they took the great circle route that I posted and not the route over the plains. Not just the lights either, the landscapes at the beginning.