Unfortunately, this structure can't really work.
Tomcat, in fact, consider all the subdirectories under the webapps directory as default contexts. In this case it considers all the <client> directories as contexts and looks for the WEB-INF/web.xml for each of them.
So, in your design, Tomcat considers the client's directories (and not their subdirectories) as web applications.
You can organize all your applications using that structure, but do not use the webapps directory (use any other location) and you have to define all the context manually in the server.xml, or just put all the applications in the webapps directory.