Ok with pictures this time.
Here's an old press, from about the time the cards were printed. This one is very typical of both lithography and letterpress presses of the time. This one is probably letterpress.
Here's the same image with some poorly drawn arrows pointing out the guide fingers/rollers that keep the paper organized in the outfeed area.
Here's a video showing a couple different presses running, including one similar to the one in the pictures that has fewer rollers/guides, but does have the running belts and a different set of guides.
https://www.net54baseball.com/pictur...ictureid=28826
With the ink wet, any of those guides can drag on the printed area causing a line.