Most probably the issue is your tomcat running on port 8080, chances are you most probably have a firewall which is blocking that port from being accessed from outside. Also some networks tend to block outbound traffic on 8080 port as this is usually an intranet port.
You could either try turning off your firewall altogether (not recommended if it is on a public domain) or you could just open up port 8080 inside your firewall.
Although not related to your problem I see you ave placed the tomcat installation inside your "/root" and most probably are running your tomcat instance as "root" which is also definitely not recommended. (In fact if you might not be aware many people are of the suggestion that using Linux with Root is worse than using Windows).
I suggest you place it in some other folder for ex: /opt/ and use some non-privileged user account (for ex: "nobody") or maybe create some non-privileged user account without login privileges to run your tomcat. Also remeber in this scenario you will have to change the ownership of your files from root to the user which you will be using to run tomcat.