I'm not familiar with the terminolgy as used in this context but I think what they are getting at is that spin is either up or down and nothing inbetween (it's dipole nature) and can cancel out while mass is always positive (monopole nature, even anti particles have positive mass) so it is additive.
In this context it is a bit like charge which averages out because of its dipole positive or negative nature, or is it tripole if we count neutral?
The statement "mass (or energy-momentum) adds up" has to be used with caution because the result of the energy-momentum equation is rest mass and does not add up in the normal way. A pair of photons can have non zero rest mass when considered as a total system while the individual photons that make up the system have zero rest mass. It would be better to consider the inertial mass represented by the energy term of the energy-momentum equation which is a scalar quantity which is directionless (scalar) and always adds up in the normal way in the rest frame of a closed system.