First, your connector is set to listen on port 80. Make sure that your test URL is addressing port 80, and not the usual Tomcat port 8080. If you don't include an explicit port ID in the URL (ex: "http://xxx.com:8080"), of course, the http: protocol will be using port 80, but it's worthwhile to make sure. If you're talking to a port and it's not a port configured for compression, then you'd certainly have a problem.
Secondly, the compression (and encryption), if any between client and server are negotiated based on what the server can offer and what the client can accept and will be the lowest-common-denominator of the two. Verify that your client can handle compression.
One thing: For Tomcat to listen on port 80 (or any port less than 4096), it either has to be running as a privileged user or using the "port 80 wrapper". Running as a privileged user is a security risk and is not recommended. Commonly, Tomcat will be fronted with a reverse-proxy server such as Apache httpd or nginx, which gives the dual advantage of being able to handle port 80 without running privileged (using resources that Java apps can't) and of being able to handle a mix of J2EE and non-J2EE apps (such as python and php).
The secret of how to be miserable is to constantly expect things are going to happen the way that they are "supposed" to happen.
You can have faith, which carries the understanding that you may be disappointed. Then there's being a willfully-blind idiot, which virtually guarantees it.