Question: Does upgrading from Tecplot 360 2011 R1 to 360 2011 R2 require a new license key?
Answer: No.
If you have a single user license then you can use the same key you are using for Tecplot 360_2011 R1 and 360 2011 R2 will run.
If you have a network license then you can point Tecplot 360_2011 R2 at the same license manager Tecplot 360_2011 R1 uses and 360_2011 R2 will run.