Definition of link gain for an optical system
It depends on what you define to be your "link". 

In general it would only make sense to define a gain over a part of your system that is linear. So it would not include a digitally modulated laser driver or a digital-output decision circuit following the receiver.

It might refer to just the transmission path: optical fiber, connectors, and possibly coupling efficiency effects at the receiver. 

Or it could refer to the laser, transmission path, and possibly the receiver. 

In many cases, you will find the "gain" of the system to be less than 1, sometimes much less than 1.


  why does the threshold current of a diode laser have no impact on link gain whereas increases in slope efﬁciency have a major impact?


The threshold current only changes how you have to bias the laser to avoid nonlinearity in the modulation (clipping). The slope efficiency is \$\dfrac{\mathrm{d}P}{\mathrm{d}I}\$ describing the gain of the laser from input (current) to output (optical power). As such, if your link is defined to include the laser, the slope efficiency will be one of the multiplicative factors whose product is the link gain.