I am basically a SharePoint developer but also an Admin by accident. I have 2 SharePoint(2013) servers (CompanyNameWeb and CompanyNameApp) and 2 SQL Servers in Production envt. Central admin url is http://CompanyNameApp:9000. Not sure when, but in CompanyNameWeb server the "Central Administration" services is Stopped. Of course the site is running fine, but does it need to be turned for good reason?
It is Fine, Typically Central admin is hosted on the App server thats why you are seeing the it is started on App server.
You dont need to worry about it, You can start the service on the web server if you want loadbalanced the CA, otherwise keep it as is.