Opening port: basic questions

opening 27030 on my computer and mapping box 27015 to local computer 27030 would have worked as well?

Yes. The server should then be set to listen on the port 27030 on the local computer (and the local firewall should be set to allow this), but a remote client should connect to the port 27015 of your external IP address.

To see if a port is open you need this port to be open IN ADDITION to have an app listening behind?

Yes. See what the documentation of nmap (a port scanning tool) says about this:

An application is actively accepting TCP connections, UDP datagrams or SCTP associations on this port. Finding these is often the primary goal of port scanning. Security-minded people know that each open port is an avenue for attack. Attackers and pen-testers want to exploit the open ports, while administrators try to close or protect them with firewalls without thwarting legitimate users. Open ports are also interesting for non-security scans because they show services available for use on the network.

A closed port is accessible (it receives and responds to Nmap probe packets), but there is no application listening on it. They can be helpful in showing that a host is up on an IP address (host discovery, or ping scanning), and as part of OS detection. Because closed ports are reachable, it may be worth scanning later in case some open up. Administrators may want to consider blocking such ports with a firewall. Then they would appear in the filtered state, discussed next.

There are more states recognized by nmap. The site you used may or may not tell all of them apart (e.g. maybe internally it does, but maybe it is designed to print "closed" for anything that is not open). My point is: the presence of a listening application makes a difference, so the general answer to your question is yes.