If the 600Ω resistor is not there, the voltage would not dissipate any power, and the dBm pseudounit would not be the one to apply.
The then applicable pseudounit would be the dBu if wanted to express in other than the real unit Volts.
The u notes unloaded, or unterminated.
If 0.774 Volts RMS are present with no resistor presence, that is called the 0dBu reference.
Edited: added---> You have been asked to make a 6W (output - not dissipation) audio amplifier.
Your input is 1 milliwatt (0dBm) . The output is to be 6 W. The power gain of the amplifier is then to be 6000.
6 ÷ 0.001 = 6000
If the amplification is set by calculating with input resistance and feedback resistance as on an operational amplifier, then you know the ratio has to be 6000.
If that IC alone can achieve such gain, you do not need a preamplifier.
If by itself that IC cannot amplify 6000 times the power, you need another stage(s)
By the way, that IC is not rated to reach 6 Watts at recommended operation...
Playing with my audio analyzer, set to 0.774 VRMS (0dBm) lifting the 600 Ω input load, the level rises to 1.48VRMS ; but I do not know the output impedance of the instrument. Added: Checked its manual, It is 600Ω