Absolutely agree, that's the way I worked when cleaning shops. You can either " capture " the gum with a vacuum, as you work, or vapourise the bulk of it and vac up any surplus.
Haven't watched the video, but I found using a rough terry towel impegnated with jel got rid of the residual, very important and probably not done previously.
I should add, the vacuuming was done using a water filtration vacuum although a cheap wet / dry vac would suffice