A Domain Name will simply resolve to an IP and has nothing to do with the port the request will actually be sent to. The port end point on the host is defined as another part of the URL.
See Wikipedia for Domain Name Purpose:
Domain names serve as humanly-memorable names for Internet participants, like computers, networks, and services. A domain name represents an Internet Protocol (IP) resource. Individual Internet host computers use domain names as host identifiers, or hostnames. Hostnames are the leaf labels in the domain name system usually without further subordinate domain name space. Hostnames appear as a component in Uniform Resource Locators (URLs) for Internet resources such as web sites (e.g., en.wikipedia.org).
And for URL syntax:
Every URL consists of some of the following: the scheme name (commonly called protocol), followed by a colon, two slashes,[note 1] then, depending on scheme, a server name (exp. ftp., www., smtp., etc.) followed by a dot (.) then a domain name[note 2] (alternatively, IP address), a port number, the path of the resource to be fetched or the program to be run, then, for programs such as Common Gateway Interface (CGI) scripts, a query string, and an optional fragment identifier.
What you might do is install a small proxy server (e.g. http://www.gcd.org/sengoku/stone/) and put your traffic through to the server running on 8050.
As you said you were running this application on a "Home Server", is it behind a router which might do the port forwarding? That would be the simpliest solution.