No, I think you've got the right idea, Navigator. Did you see the other pics here:
http://bysteso.blogspot.com/2015/04/blog-post_7.html -- that show a little more about how she uses the cutter? I do think the wire slices vertically, using the edges of the two uprights to guide the wire.
The very last photo in her tutorial hints at how she set up an older version of the cutter to take a 4 mm horizontal slice off the bottom of a soap log. You could cut grooves higher up to take thicker slices.
I would think it would take two people -- one to hold the cutter in the grooves and the second to push the log through. Unless she has a way to fix the wire in place so it doesn't pop out of the grooves -- she doesn't mention anything about that. The way I'm understanding this is the soap would want to push the wire out of the grooves as the cut is made.