Symantec Protection Engine 8.0
Symantec Protection Engine 8.0 comes with the cloud-based centralized management and reporting console. JRE is not mandatory either for scanning or monitoring. It is completely optional. You need JRE only if you want to use on-premise console.

Symantec Protection Engine 7.5.x and 7.9.x
You can install Symantec Protection Engine 7.5.x and 7.9.x in two modes – a) Core server only mode (without on-premise console) and b) Core server with user interface mode (with on-premise console). 
JRE is not required for scanning and is completely optional in Symantec Protection Engine. You need JRE only if you want to use Core server with user interface mode with on-premise console.

Symantec Protection Engine 7.8.x
You can install Symantec Protection Engine 7.8.x in Core server only mode. JRE is not required because on-premise console that requires Java is not available in Symantec Protection Engine 7.8.x.

Symantec Protection Engine 7.0.x
Symantec Protection Engine 7.0 requires JRE to function. If you do not want to depend on JRE, you can upgrade to Symantec Protection Engine 7.5 (32-bit).  We recommend you migrate to the latest version of Symantec Protection Engine.

See Symantec Protection Engine Java Support Matrix.

As described in this article, JRE-based functionality is completely optional. Symantec does not provide a license for JRE.  You must buy it separately from Oracle.