Tenkara guides used to have a good doc on fighting big fish. It is no longer available.
here is some stuff but not as good as that original doc.
http://www.tenkaratimes.com/tenkara-blog/archive/bigfishtenkara
Things to note. try to avoid high sticking. Pushing the rod to or beyond vertical. Yeah I bunch guys say show the fish the butt of the rod…but to me that is plain bad advise…or mis leading. You want to put pressure for sure but not over tax the rod.
Not sure of the source but regarding large fish…sometimes too much pressure can aggravate the fish. Slow constant pressure can wear a fish down over time…a fish that out matches your equipment. The idea being, cause and effect. You put the boots to the fish…you may get boots back. In close quarters you may need to beef up the rod to match your target.
In the video you posed above…look at the angler. During the initial fight the rod fighting angle never passes 45-60 degrees or so. Its only when the fish is defeated does the rod break the fighting angle
Most rods can never achieve close loop not even close. Tenkara rods are very flexible but if you push them too far they will fail. Tippet breaking strength and suggested tippet ratings for rods are all over the place.
Tenkara rods are made for small to medium trout. Can you catch bigger…yes, but they are exceeding their purpose.