I suppose I'm not really clear on what a "vicinal railway" is--it looks like the rails run alongside the tracks, not directly in them. Plenty of short-line industrial railroads ran in the streets in American cities, serving local industries. Some were owned by larger railroads, others were independent operators serving the local community. In San Francisco, there was an industrial belt line running through Fisherman's Wharf that was taken out about 20-25 years ago. (Incidentally, cable cars were not unique to San Francisco: they, along with rail-borne horsecars and steam dummies, were common in many cities until the introduction of overhead trolleys in the 1880s.)
In many places, railroads run alongside roads, but frequently the railroads were there first.