The September 1 start date is a bit odd, since Windows Server 2016 isn't "launching" until the last week of September at Microsoft's Ignite show, and won't be generally available until early October 2016. (I guess the extra month up front is for those who want to kick the tires of the latest Windows Server 2016 technical preview before committing.)
The fine print of the offer also stipulates that customers who switch workloads to Hyper-V only qualify for free Windows Server 2016 Datacenter licenses when they buy Windows Server Datacenter plus its Software Assurance volume-licensing plan -- meaning customers still have to buy Software Assurance to get the free license to Datacenter Server.
The downloadable data sheet about the migration offer notes that in addition to the free Windows Server Datacenter licenses, participating users will get free online training through Microsoft Virtual Academy. The offer ends June 30, 2017.
Windows Server 2016 Datacenter is one of a handful of Windows Server 2016 editions Microsoft will be releasing this year. The Datacenter version is for "highly virtualized datacenter and cloud environments." Other editions include Windows Server 2016 Standard, Essentials, MultiPoint Premium Server, Storage Server, and Hyper-V Server.
On the licensing front, Windows Server 2016 Datacenter and Standard will be licensed by core; Essentials, Multipoint Premium, Storage Server are licensed by processor, as this chart from a recent Microsoft Australia OEM Team blog post makes clear. Users who want to deploy Nano Server mode -- whether on Datacenter or Standard -- need to have Software Assurance coverage in order to do so.
Nano Server is one of three installation options in both Windows Server 2016 Standard and Datacenter. (The other two are Server with Desktop Experience and Server Core.) The Long Term Servicing Branch option is not available for Nano Server, and the more frequently updated Current Branch for Business servicing model is not available for Server with Desktop and Server Core. See this blog post for more details on the coming servicing options.
Datacenter Edition allows users to run an unlimited number of operating system environments/Hyper-V containers, while Standard Edition allows only two. Datacenter Edition also includes features like Storage Spaces Direct and Storage Replica, Shielded virtual machines, and a networking stack, which are not part of Standard Edition.