How to change the specific game config (and therefore port) will depend on which game. Probably each game has it's own method. Some perhaps don't even have the ability to configure that?! So to configure the specific game, you'll need to research it.
Another path would be to use a system tool to redirect the traffic to alternate port. You could use the firewall to do that. Webmin (https on port 12321) has a UI for firewall rules.
That will depend on which game or do something system level
How to change the specific game config (and therefore port) will depend on which game. Probably each game has it's own method. Some perhaps don't even have the ability to configure that?! So to configure the specific game, you'll need to research it.
Another path would be to use a system tool to redirect the traffic to alternate port. You could use the firewall to do that. Webmin (https on port 12321) has a UI for firewall rules.
There are a ton of other options.
If you have issues trying to do one of the specific options, please feel free to post back.