Those used to appear on the official State of NH rail map until they cleaned it up to just the state-owned railbanks last year. It's GIS noise on the map from folding in old topos into the data layers. The land ownership on the branch to the Cog Railway, for instance, was long ago absorbed by the widened access road even though there are some rail structures still extant on the side of the road recycled for sidewalks and culverts. So while the access road makes the grading very easily traceable, there are no extant property lines today that allow it to be legally classified on a DOT map as an intact ROW.
Since a lot of online maps--from Google to the official state DOT's--share the same public data you can sometimes get these 'phantom' rail lines showing up that haven't existed since the Depression and have no extant property claims for continuing to show the ROW on a modern map. Google has done a good job over the last couple years scrubbing its data layers clean of legacy crud, but YMMV depending on what data dump anyone else has sourced (or if they're still using a 'polluted' Google data layer from before the mass cleanup). The MassDOT rail map takes that to an extreme. It's both a one-stop treasure trove of GIS traces of every ROW dating to the mid- 19th century and an unnavigable mess that's about as accurate as a carnival hall of mirrors because they just tossed every era's topos into a blender, puked it out onto one PDF, and called it an "official" rail ROW map. It's got so many phantom, mis-classified, and formerly relocated ROW's on it from old topos that it's basically useless for tracking anything that isn't bona-fide active or under official state landbank. Many of the gradings depicted don't even physically exist anymore because of earth-moving from subsequent construction, but the ROW's still appear on the "official" map regardless.
It's a real problem in the world of GIS systems on how to scrub all this needle-in-haystack spurious data that affects the accuracy of overall navigation...without investing in huge quantities of human work hours to go comb through the layers and edit out the 'phantom' objects. One of the reasons why you've got crowd-sourced OpenStreetMap and...now (in its infancy) OpenRailwayMap
. Those croudsources popped up as a means of distributing that heavy-lifting human cleanup work on a massive scale and slowly stamp out the inaccurate data layers (old pre-cleanup Google Maps & the like) that keep gettting recycled anew with the same errors and 'phantoms'.