How to use iCloud calendar without having an Apple device
Unfortunately you can't add iCloud Calendar support to an Apple ID without turning it on via an iOS or Mac device.
You can borrow someone's Apple device and turn it on for the Apple ID in Settings > iCloud, on an iOS device or System Preferences > iCloud, on a Mac.
Once you have turned on "Calendars" for the device, you can immediately disable it and sign out of your boss' Apple ID, and your boss should be able to access iCloud Calendar from www.icloud.com.