Why thank you, cyberderf!
I am not entirely about the 'screened lines' you refer to, as the image in the screenshot appears smooth to me. However, I do believe I know what you're talking about, as the finished versions at [link] and [link] do have an alternating pixel lines effect. I did this simply by using The Gimp's "Stripes Fine" pattern fill on a layer behind the subject image.
Hope this answers your question. If not, let me know!