I think they're referring to the fact that there is one dimensionless base unit already standardized in SI: the mole. There aren't two length units, so there "shouldn't be" two dimensionless ones.

(Whether they were trying to be funny or not I couldn't tell you.)

The "mole" is the unit, "mol" is the symbol for the unit, like with "kilogram" and "kg".

How do you know that lalaithion was not trying to amuse anyone?