The AltTester Desktop app needs to be running for the AltTester SDK (running inside the app/game) to connect to it.
The AltTester Desktop app contains a web-socket server (AltTester Server) that facilitates the communication between your tests and the game/app under tests, and it needs to be always running while tests are performed.
By default, both the AltTester SDK and the AltTester Desktop use port 13000 for the communication. When the AltTester Desktop is running and the connection is established, the text on the green popup inside the game/app will indicate that the SDK is connected to the server running on port 13000, instead of the "Waiting to connect to AltTester Server on 127.0.0.13000" message.
More info on the architecture is available in the documentation here: https://alttester.com/docs/sdk/latest/pages/overview.html