Are there any other causes, apart from the specific port to be reached being closed, that can lead to an ICMP Destination unreachable - Port unreachable message? What are possible reasons for this type of ICMP message?
That is exactly what it means. The message is from the destination host saying that the original datagram is unable to reach the port on the destination host.
The IP packet made it to the IP process in the network stack of the destination host, but the transport protocol rejected the transport datagram, sending back the ICMP error message..