I agree with John - the pattern of 12-13 'stripes' from top to bottom of the stamp is from how the gum was applied. You may also notice, in the other direction, 4 or 5 'waves' from side to side. Those are a remnant of the Rotary Press. Laid paper is from the paper manufacturing process - this is not on laid paper. There are all kinds of things that can easily be confused with being all kinds of other things.
The small vertical lines are from the web fed Stickney rotary wet printing press gumming station gum rollers. A large horizontal line or large horizontal lines are from Stickney wheel and bar perforator gum breaker bars.