Does SQL Server 2016 Standard Edition support table partitioning?
Starting with SQL Server 2016 SP1 the Standard Edition supports all functionality most programming surface of the Enterprise Edition, as announced here: SQL Server 2016 Service Pack 1 (SP1) released !!!. 

Quoted from that article:


  The following table compares the list of features which were only available in Enterprise edition which are now enabled in Standard, Web, Express, and LocalDB editions with SQL Server 2016 SP1. This consistent programmatically surface area allows developers and ISVs to develop and build applications leveraging the following features which can be deployed against any edition of SQL Server installed in the customer environment. The scale and high availability limits do not change, and remain as–is for lower editions as documented in this MSDN article.
  
  


What still differentiates EE from SE are primarily performance and administrative improvements. 

So, in your case, SE will support table partitioning (functionality) but will not leverage certain performance enhancements available on partitioning, like 'partitioned table parallelism'.