Its really simple you just need to slip on a short section of downpipe - as per my white lines. Do it at that still frame position taken from the vid as it also looks like the swan neck and downpipe could be a little short. Don't cut the short piece of downpipe too long otherwise you will make a high spot at the running outlet. You may be able to do it all in situ with a bit of swearing.
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Wouldn't the diameter of the small section be the same as the outlet on the running gully? If so, whilst it would fit in the elbow. it won't attach to the outlet.
Personally, would just use a small screw to secure the fitting.