There is an executable for all three platforms, which runs inside a terminal window. There is no extra webserver like Apache or NGINX needed. A webserver on port 3000 is started by simply executing the downloaded file. The default port can be changed. If you want to know how to change it, look at the advanced configuration.
There is also an official docker image available. This image gets automatically updated with each commit on Github. So if you want to use always the newest version of the TS3 Manager, this is the way to go.