Chrome on Linux will not work with Java, as NPAPI support was dropped in Chrome 35.0. As such, you will need to use Firefox.
It seems like you do not have the Java browser plugin installed. You can install Java JDK 8 and the browser plugin from the Web Upd8 Java PPA. Open the terminal and enter these commands in, line by line:
sudo apt-add-repository ppa:webupd8team/java
sudo apt-get update
sudo apt-get install oracle-java8-installer
After that, you will have to add your WebEx domain to the Java plugin's Exception Site List. To do this, open "Oracle Java 8 Plugin Control Panel" and click "Edit Site List" under the Security tab:
After that, click "Add" and enter the domain that your WebEx meeting has: (I'm using the WebEx test meeting as an example here)
After you're done, click OK and OK to exit and save changes. Open Firefox and browse to your WebEx meeting link. When you're prompted to allow Java to run ("Activate Java"), click either "Allow Now" or "Allow and Remember", depending on your preference.
At this point, the Java loading screen will show, and a security warning should pop up soon. Check "I accept the risk and want to run this application", and click Run:
A progress bar will show up and the WebEx meeting center will show up soon too, if everything has been successful.