My in-laws live just off of MA 88. The in-the-field situation is just like as described above. Furthermore, MassDOT GIS shapefiles concur with the southern end of MA 88 being just south of the rotary, at Milepost 0.
My guess is the list file was created down to East Beach Rd because that's where OpenStreetMap shows MA 88 as extending to. But the evidence as explained does not fully agree with that, especially MassDOT's GIS files which explicitly show it as "not a numbered route".