It is indeed the old ROW of the old Berkshire Street Railway --- its Huntington branch, in particular, which opened in 1913 and ran for only a couple of seasons, hauling both passengers and freight. It was owned by the New Haven and was intended to compete with the B&A, which probably doomed it from the get-go. It wound through a sparsely populated area that included only three small villages (East Lee, Blandford [North Blandford, specifically] and Huntington). I've never been entirely clear on whether it continued southeast from Huntington all the way to Westfield; I believe that was the original intention, but I've never fouhd clear evidence that the line went the whole distance.
The roadbed can be very easily traced. It runs, as you said, roughly parallel to Route 20 to a point just up the hill from where Route 8 veers off to Otis. It crosses under the highway via a partially-filled in overpass and from thence to the corner of Johnson Road and the Lee-Westfield/North Blandford Road (see DeLorme's Massachusetts Atlas and Gazetteer). It parallels the Lee-Westfield/North Blandford Road and can be easily seen as there is a power line running along it. I haven't traced it east of North Blandford, but I know it makes a long descent --- a rather precipitous one at that --- down toward Huntington village.