It is actually CSXT property, and is referring to as the South Boston Running Track, or some MBCR dispatchers also refer to it as the Neponset Industrial Track. The track used to go all the way out to the piers at Black Falcon, much of the rail is only covered in small portions. As a part of the Big Dig the track was reinstalled behind the Seaport hotel area after the tunnel work was done, but nothing has gone down there. There is supposed to be new business going down there in the future, but I haven't heard anything on that lately. At the other end the line connects to the MBCR's Middleboro Main-Line at "Fly" interlocking. There is 3 track yard which is now basically used as a place to run-around cars after servicing the Boston Globe. There is also a hand-thrown switch connecting the line to the Middleboro Main right by the Red Line and Haul Rd bridges, but this switch, aka the "Old Way" is only used by MofW crews when hi-railing.
As for Boston Rail Terminal, he was evicted months ago and should be getting all of his stuff out of there, which hasn't happened yet. There are also 2 threads about the BRT in the New England Railfan Forum.