The traffic referenced in the NAT entry must also be allowed in the forwarding chain. Make sure that overall you are allowing the traffic in the forwarding chain remembering that destination entries should match the DST NATed addresses since the forward chain filters occur after DST NAT.
I am using a simple application to try to establish a connection to the server using a TCP-IP socket. When the NAT rule I use is enabled I can see clearly how there is some traffic arriving to the server, and the application waits for some time while trying to connect to the server, but it fails. When the rule is disabled, the program immediately prompts a message indicating that the connection was refused.
From this I conclude that I am able to send data to the server, but it is unable to respond to the client to establish a connection.
If you DST NAT traffic to a server it will still appear with the original source IP (unless you also SRC NAT the traffic) so the server needs a route back to the originator. It looks like you have no default route set on the server.