You stack the strings in the gripper to get two in at the same time to set the Anchor clamp. You don't have to do it that way, but it's easier.
The other way is to clamp the untensioned string like in the video, (let say the left side) and pull the right side main. You may want to hold the clamp up to the level of the string bed while tensioning. Or else it will drop below. Once you have tension. Clamp off the right side and both clamps should have tension. Then continue like in the video.
The reason you don't want to pull directly on a clamped string without going through a grommet loop is it may slip and damage the string. Some people use a starting clamp behind the anchor clamp to keep the string from slipping.
Machines: Gamma 6004 2-point w/ Wise 2086 & Babolat Sensor Dual