Ein deutscher Tourist beschwerte sich.
This simply means that there was a German tourist who complained.
Der eine deutsche Tourist beschwerte sich.
This implies that there was more than one German tourist (most likely two), and one of them complained.
So the first sentence translates to: A German tourist complained. The second translates to something like One German tourist complained [and the other(s) didn't]
Another possibility is that there was only one German tourist and that this tourist complained. Without context it is impossible to tell which meaning is the intended one.