I'll have to watch the video later, but I'll throw in my 2 cents. I've field dressed (gutted) deer with everything from a 2" gerber folding knife to an 8" KaBar. What I learned is you can have too little and too much knife for the job. What works well on one animal may be inadequate for the next.
Personally, I like to get the animal dressed and chilled as quickly as possible. It makes a difference in the quality of the meat. The best knife is the one that you are comfortable with and is sharp. For deer, it's not necessary to split the pelvis or sternum, although it can make some tasks easier. But it's not necessary.
I harvested two deer this year and dressed both with a knife I forged, that's sharp enough to shave with. (Photo attached if I can get it to work from my phone)
The way I was taught and find most effective for the way we handle and process deer is to start at the anus, or vent if you prefer, and cut around it just through the skin. Once through the skin I begin working around it pulling the vent to one side and cutting until it pulls freely from the cavity. Some folks will use string or zip ties to tie it off so it doesn't drain anything out onto the carcass. I then split the skin from the anus up past the ribs until I can reach the esophagus at the other end. On this cut I try to be careful to only cut the skin and not the lining that holds in the organs. After cutting free the esophagus and all that comes through the front of the rib cage, I will then split the lining and peel the diaphragm so it's loose. At this point, if you did everything right you can reach in from the middle of the animal with one hand and grab the esophagus and then grab the intestine/colon right before it goes through the hindquarters with the other hand and pull everything cleanly out.
A rinse with a hose is a nice finish and then we hang the deer, weather permitting, for up to 14 days. Most of the time the weather only lets me get about 3-5 days of hanging before butchering.
And that turned into a far longer post than I thought.