Mossberg 930, 18.5" barrel, cylinder choke, 12 ga. Maverick 88, 18.5" barrel, cylinder choke, 20 ga. Both demonstrate results consistent with the video in real life. 12 ga, #00 buck, 20 ga, #4 buck. Both are intended for this type of use (I gather).
For us, the issue isn't really patterning at close range, it's the barriers in our house. Given our primary defense plan involves a tight hallway and staircase, a handgun is a better choice for us.
If I needed to confront an intruder in one of the larger areas of our home, indeed a shotgun would be preferable. Unfortunately, I can't expect an uninvited "guest" to voluntarily agree to limit a potential confrontation to those areas. My XDm .40sw gives me a solid 15 chances to discourage an intruder, the 930 gives me 8. The 88 gives us 6, the Canik my wife has gives her 21.
That aside, an intruder is more likely to be convinced to retreat if she is holding the 930 than her pistol, I will grant you that. Given that in that situation we want the intruder out, rather than shooting them, it would tend to tip the scale toward the shotgun.
As with anything, there isn't a "one size fits all" solution. Each person needs to evaluate their situation and choose accordingly. The primary takeaway for me from the video is to know your weapon and train with it. But that is true for everything we may choose to protect our family with. The time to learn the capabilities of our defensive weapon of choice isn't when a bad guy is in your house.