On second thoughts having looked more closely at the manual - it's really unclear there.
The diagram showing all the parts of the seat shows the circular/oval holes, like the seats Margaret shows in the video, and labels them "Passage of seat belt".
However the set of diagrams in the instructions as to how to fit the seat seem to ignore the circular holes entirely, and refer to some kind of slot in the base of the seat, which would make it impossible to use the circular holes in the way shown in the video.
The shape and general fit of the seat definitely fit the pattern of car seats which are fitted the video way. And it doesn't have any belt lockoffs, which are usually present when a different seatbelt path is used. I'm actually concerned that the fit shown in the manual doesn't seem to have any way of securing the belt at all, so the seat will be very loose and not safe.
Honestly, this is very strange. I've read a LOT of car seat manuals and I have very rarely seen one as contradictory as this.
If I needed to make an educated guess, I'd do it the way as shown in the video, but I can't recommend that with confidence, because going against the manual is never recommended. It might be worth contacting The Nursery Store's customer service to see if they can clarify, though my concern there is that they won't actually know the answer because these seats are designed and made by another company, they just market them.
Do you need to use the seat urgently?