May I use BizTalk Server 2013 R2 Enterprise with a Visual Studio Enterprise with MSDN subscription on test and development devices during the contract period?

Yes, you may. For this purpose, Microsoft provides a comprehensive overview, which can be obtained from the following link.

https://www.visualstudio.com/en-us/products/subscriber-benefits-vs.aspx

For confirmation of the BizTalk Server 2013 R2 Enterprise, see line 110 of the table. The current version of this overview (July 2016) is attached to this Use Case.