What is the exact definition of propagation constant of a two-port network?
You can define 2-port networks with a variety of different parameters sets. 

If you define a 2-port with Z-parameters, then the inputs are the port currents and the outputs are the port voltages.

If you define a 2-port with Y-parameters, then the inputs are the port voltages and the outputs are the port currents.

You can also define hybrid (H) parameters that take V as input on one port and I on the other.

Or ABCD-parameters where the voltage and current on one port are taken as the independent variables and the voltage and current on the other port are the dependent variables.

Or S-parameters that take inward-travelling waves of a given characteristic impedance as inputs and get outward-travelling waves as outputs.

The source quantities are, presumably, the inputs to your 2-port model, for whichever type of 2-port model you are using.

But frankly, you're unlikely to ever see this \$\gamma\$ again. So just take it as a defined variable for explaining the particular type of network you're researching, and don't worry too much about  how it applies to other types of networks.