My question is: what exactly is the "supported lifetime for the device?"
Is this "supported lifetime" defined by the manufacturer's warranty? The original OS date of installation? Something else?
It means if you install Windows 10 during the free period, it will be as if you bought a normal Windows license.
If they meant that, they would have said that. There's a reason they chose the language they did.
Check http://windows.microsoft.com/en-us/windows/lifecycle for the current list of Windows.
"Supported lifetime for the device" does not necessarily mean "supported lifetime for Windows 10." Although your interpretation may be correct, they have (intentionally or otherwise) used ambiguous wording in how they describe this.