Download Celestia, which is a 3D planetarium program. Navigate to the higher latitudes and you will find that there is no zig-zagging sun. The sun floats above the horizon around the observer just as expected:
I did. I found a "zig-zagging" sun, just as with the AndrewMarsh app you linked to earlier.
Allow me to decipher your Celestia screencap and explain:
You had the red line of the sun's ecliptic displayed against a blue equatorial grid and a horizon reference for the earth.
My image takes the same snapshot and adds some elevation above the horizon lines (green) and an apparent path of the sun (white) in reference to that those.
Your snapshot was from a point in time 2 hours after the sun had reached its lowest elevation on that date, as seen from 75° north latitude. At the time of the your picture, the sun is ascending. It was ended its "zig" 2 hours earlier and is now on it's "zag."
Though this is for 2014, look at how the Andrew Marsh calculator depicts that: the sun is "zigging" just prior to reach N where it will reach it's lowest point over the horizon, and then will "zag" as the elevation increases over the next ~12 hours.
Checking this with Stellarium, and it's the same story. I put all 3 grids in (equatorial, azimuthal and ecliptic) so you could see how they are related.
This is what is happening in the opening video you posted. I wouldn't call it "zig zag." More like "undulating" but it's not "smooth." The "zig zag" is a function of latitude. At 75°, it's "zig zags," as illustrated by the resources you brought to the table.