A little variation isn't the end of the world.
Part of the reason that we generally try to allow about 1/8" of "extra" space is for minor variations in the materials.
Maybe the glass is 1/16" uneven, or the frame might be a tiny bit skewed, or some other measurement is just slightly off.
As long as your material is not tightly fit within the frame, 1/16" variance shouldn't be a big problem.
But it is better to have your equipment working at its best.
1-make sure that the bottom rail that the material rests on is perfectly square to the cutting head rails. There are two Allen head screws that are tightened to hold that bottom rail in place. Use a large construction square to check alignment, loosen the screw furthest to the left, adjust the rail up or down as required to make it square, and retighten the screw. Make sure that you don't get the left and right horizontal rails out of alignment while doing this. You want them to be as closely horizontally aligned with one another as possible.
2-use a scrap of 4ply mat board as a slip under matboard or foamboard, it makes a smoother finished cut. The blade doesn't need to ride inside that channel, as long as your other adjustments are accurate.
At about 1:45 you mention "give" but it isn't evident what is happening in the video. Do you mean the cutting head "wobbles"? Or the rails are loose?
3-you probably have already done it, check all the screws holding the cutting head rail and the screws on the cutter itself, for tightness.
Not sure why the head would lift (pop up) like that?
Does it happen in exactly the same place when moving the head up and down?
Does it happen anywhere else from the highest to lowest ends of travel along the rails?