Why do you call the reference in fig. 20.14 a Beta-Multiplier Reference (BMR)
instead of calling it, as you show on the top of page 625, a constant-gm 
reference?

The BMR is only a constant-gm reference when the MOSFETs follow the (long 
channel) square-law equations. Since CMOS circuits in production for the 
last 15 years or so can't (accurately) be described with square-law equations 
it's best to describe the reference by how the MOSFETs are related (ones Beta is
multiplied up from the others).

Also note that the name BMR is similar to the name BGR (bandgap reference).