How can I expose non-80/443 TCP port to the Internet?

My mobile application needs to talk to a service running on Platform via non-80/443 TCP port. How could I expose that port?

You cannot. Platform.sh is a web-centric host. The only ports that are exposed to the world for incoming requests are 80 (HTTP), 443 (HTTPS), and 22 (SSH). All other ports are hard-blocked at the network layer.