My spouse showed me that video a couple days ago - and I must confess, in 40 years of mask wearing I never really thought that I had laxity between the mask edge and my cheeks, but the physician in the video certainly did demonstrate laxity.
I wonder if some of the issue is a one size mask for faces of significantly varying sizes.
The trick she presents seems simple enough and seems reasonably effective - BUT - I think in less dextrous hands it MIGHT result in tearing or damaging the mask. The reason I have this concern is I recently was removing a mask made by an over seas vendor, very carefully, and found just pulling the elastic from around my ear, I rendered a tear in the edge of the mask, between the elastics - this was not a violent, or hard pull, but a very gentle one, but nonetheless, the edge of the mask was torn for about an inch, effectively reducing its utility almost 100%. Remember, I wore surgical masks for almost 40 years, so I do have some previous experience at successfully removing masks without tearing them.
In an ideal world, we would all be using these masks as single use items ( like in surgical suites ) - but in todays pandemic coated world, I suspect many folks are reusing their masks several times - and when one re-uses their mask they greatly increase the likelihood they will contaminate their hands with any virus trapped by the masks filtration.
I think if one's mask is too loose between the two ends of the elastics, like the physician's in the video you linked, tying the elastics together AND tucking the fold inside the mask, as she demonstrated may be quite helpful, but I would suggest that folks be very careful and pay close attention, especially if their hands are much larger and less dextrous than hers...
And I do think, some masks being provided today are significantly more fragile than was typical of routine hospital provided sugical masks in years before this pandemic.