Can I limit the ports people can access from my DNS adress?

here is my issue:

I am hosting a few game servers for me and my friends, one of these have gotten a quite large player base of random people.

I have a DNS adress in the style of beta.mydomain.com which goes to a test server hosted in my home instead of the usual one with a hosting company. I want people to be able to access only one port of my network, but I share it with my landlord and everyone who lives here (still have full access to the router though) and they host a small website with images of the rooms they rent out to students.

As it has info about the rooms for rent it has info about where I live and phone numbers to people here I wouldn't want to share. The DNS provider does not allow me to change this on their end without a costly upgrade, so is there any way I can block access only if it is accessed using a certain adress? I don't think my landlord would want to shut their site down or switch to a non-standard port.

TLDR, I want people to still be able to connect to my test server without being able to access my landlord's website if they type it in a web browser. I have full access to my router but my DNS provider will not let me lock it on their end.