#Mostly#
Mostly
I regularly install Team Fortress 2 (another Valve game) on both Linux and Windows machines (but haven't tried macOS) and use the same backup. The game installs all the data files but the executables (files made for the specific OS) and any updates that have come online since the backup was made would be downloaded which are considerably less than downloading the whole game. All in all the most I've seen being downloaded are a few hundred MiBs.
Also note that Dota 2 shares a lot with other Valve games since they are all made with Source, Valve's game engine.