There appears to be a known issue in the headless build facility that results in a built RCP product not having a JRE (even though the product configuration indicates there should be one).
If you do an export from the Eclipse UI, you do get the JRE included.
After a fair amount of digging I figured out how to resolve this problem.
First … you need to have your product based on features.
Next, modify your features build.properties file to include the following line …
This will cause the generated build script for the feature to copy the JRE that is executing the compile into the jre directory of the product.
Obviously this entry is specific to Windows 32bit compiles.