Playing cards use this style of lettering. Not sure how far back that goes but I kind of doubt they all derive from Gorton's specific engraving machines.
> And here's A TEXT-BOOK OF FREE-HAND LETTERING, part of the TECHNICAL DRAWING SERIES, first published in 1895:
Called out in the article - "but I know simple technical writing standards existed already, and likely influenced the appearance of the newfangled routing font. [photograph captioned: From a 1895 “Free-hand lettering” book by Frank T. Daniels]"
I know it was a long essay and I skimmed most of it myself. But the author definitely mentions this and even has a picture from the 1895 book you linked to.
I also believe that it's more likely that the font was informed by what was commonly taught as good lettering for technical drawings in that era.
For example, consider the one-stroke gothic lettering in 1883's Standard Lettering, published by the Columbia School of Drafting:
https://archive.org/details/standardletterin00claf/page/42/m...
And here's A TEXT-BOOK OF FREE-HAND LETTERING, part of the TECHNICAL DRAWING SERIES, first published in 1895:
https://archive.org/details/textbookoffreeha00daniiala/page/...
Consider the "single-stroke lettering" suggested in that texbook:
https://archive.org/details/textbookoffreeha00daniiala/page/...
https://archive.org/details/textbookoffreeha00daniiala/page/...
Also consider the model forms for pre-penciled gothic lettering:
https://archive.org/details/textbookoffreeha00daniiala/page/...
It seems that such lettering was already common when the machines were introduced to produce similar lettering.