You'll need to install a JRE to provide Tomcat with a Java Virtual Machine. Download and install the 64-bit version of the Java SE Runtime Environment 11.0. The Oracle Java SE download page has the latest release available:

This release of Arbortext Publishing Engine was tested using release JRE 8.0 Update 181 (also known as 1.8.0_181), the latest available at the time of testing. If you choose a later release, it's likely to work for Arbortext Publishing Engine, but it can't be verified without formal testing.