I have Samsung Galaxy S3 and it was not showing in the "Remote devices" tab nor in chrome://inspect. The device did show in Windows's Device Manager as GT-I9300, though. What worked for me was:
cmd.exe
cd "C:\Program Files (x86)\ClockworkMod\Universal Adb Driver"
adb devices
I'm not sure if it affected the whole flow somehow, but at some point I've installed, and later uninstalled the drivers from Samsung: http://www.samsung.com/us/support/downloads/ > Mobile > Phones > Galaxy S > S III > Unlocked > http://www.samsung.com/us/support/owners/product/galaxy-s-iii-unlocked#downloads