I have a Steam Link connected to my TV which is 1080p. The Steam Link is connected via ethernet cables to my PC, and my PC has two monitors, one with 1920x1200 resolution and one with 2560x1440. As the Steam Link works by sending the picture from my PC to the TV, does the resolution of my PC monitors affect the performance? Does it render the game in 1440p on my PC, then send and downscale it to 1080p for the Steam Link? Would I be better off setting the resolution on my main monitor to 1920x1080 instead of 2560x1440 when playing through Steam Link?
Your desktop resolution shouldn't matter, but your in-game resolution will affect the performance.
Steam link scales whatever resolution to 1080p, but your PC still has to render the games at whatever resolution you have it set to, so, a higher resolution will look better, but at the cost of performance, just like it would if you were playing directly on the PC.