Answer
No — the IFS Enterprise Explorer client itself is built on and uses the .NET Framework, not the Java Runtime Environment, so running IEE itself doesn't require a JRE or any associated JRE licensing consideration. However, certain OTHER IFS application components ARE Java-based and do require a JRE to run, the Print Agent being one confirmed example, so while the primary EE client doesn't need JRE licensing consideration, other specific components of a full IFS deployment may still need it evaluated separately.