Which SQL Server 2016 edition is included in the Analytics Platform System (APS) and does this require a specific licensing model?

With APS, you are entitled to use a special SQL Server version (SQL Server Parallel Data Warehouse) which is designed for high performance in Data Warehouses. With regards to licensing, Microsoft will count a SQL Server 2016 Enterprise with Software Assurance license. Therefore, all active servers need to be completely licensed, whereas passive servers do not need to be taken into account due to the Software Assurance.

Source: Microsoft SQL Server 2016 Licensing Guide as is 2016-08-28