Yes - if you keep the boundary fixed where it is, and push up a part of the grid in the middle, the members have to stretch, and what you get is more like a tent than a gridshell.
I think the intention of the person that made that example was that you use the slider near the top that is moving the boundary anchors inwards, which pushes the gridshell up into shape.
The upwards vertical load in the middle is just there to make sure the form-finding buckles in the correct direction (because otherwise it could just compress in a flat plane, or buckle downards). The idea is that you use the slider to nudge it in the right direction once at the start, then set it to zero.
You might also use something similar for the actual erection of the real structure - using temporary jacks/scaffold to lift up the interior part, bringing the boundaries horizontally inwards and fixing them in their new location, then removing the interior support.
After it has been pushed up, what keeps the built gridshell up is the active bending of the laths, which are prevented from flattening out by their fixed supports on the ground.