You have installed a program that either requires a specific version of Java or requires a Java Virtual Machine (JVM), or requires a 32-bit version of Java.
When you go to Java.com, the only thing you are installing is a Java Runtime Environment (JRE) which supports plug-ins in the web browser. If the program needs to run java code that is on your computer, the plug-in is insufficient.
The legacy Java 6 released by Apple years ago will often solve all of the above issues as it would be the version the software was hard-coded to use, has a 32-bit version, and includes both the JVM and JRE.
https://support.apple.com/kb/DL1572?locale=en_US
If you want to use a more recent version of Java, then you can try downloading the Java Development Kit from the Oracle website (search for Java SE JDK).
However, if the program was coded poorly, it will only work with Apple's Java 6.