3 days ago Google announced support for shutters:
These are the sixteen new device types added: Awning, Boiler, Curtain, Door, Garage Door, Gate, Hood, Lock, Microwave, Pergola, Security System, Shutter, Shower, Valve, Water heater, and Window.
According to the official Google Home dev docs they should be available:
Might be that Athom needs to implement them.