Hi.
spur, I think your doubts are reasonable and equation 11.7 is indeed incorrect (but it can be applied in this case). I'll try to show this using two-port equivalent model of the the common-source amplifier with source degeneration (attached figure).
Ro is output resistance (3.59), Gm is transconductance (3.55), Rdrain - resistor connected to the drain. Iout1 is output current with short-circuited output (Iout1 = Gm*Vx). Iout in the Figure 11.4 can be identified as Iout2. Using equation for current divider: Iout2 = Iout1*Ro/(Ro+Rdrain) = Gm*Vx*Ro/(Ro+Rdrain). Gm in the example 11.1 is defined as Iout/Vx (Iout2/Vx). Using previous equation we get Gm(11.7) = Gm(3.55)*Ro/(Ro+Rdrain). Thus when Rdrain has order of magnitude comparable with that of Ro equation 11.7 will give significant error. But in the example 11.1 Rdrain (R3) is resistance of diode-connected transistor (1/gm3) and in most cases Ro >> R3 = Rdrain, which means that Gm(11.7) = Gm(3.55).