That is a bad one, good call in asking this question. I downloaded, reduced the size, and marked the root at the point you should make a cut to sever the bulk of that root. Where it has already embedded in the tree you'd do more harm than good if you tried to dig it out. The tree will eventually grow around the root completely and be fine, but it wouldn't survive being surrounded by the girdling root the way it is now.
Use a small keyhole saw or something that will let you cut precisely and lift that root out of the hole before filling it back in with dirt, making sure to leave the root flare exposed. It looks like the root flare is below the level of this root, so I'd leave that embedded part of the root in sight.
GirdlingRoot-1.JPG [ 397.07 KiB | Viewed 158 times ]