Constrain the lifetime of the demo server

Demo server was being deleted and recreated every time the lobby was
constructed, so it was always active. This rendered the "are we playing
a demo" checks useless as they always assumed we did. Logs didn't work
because of it, for example.

Construct the demo server only when the user selects demo playback, and
destroy it during the destruction of courtroom.

Make log_filename based on the application path, so `logs` subdirectory
is created relative to the executable rather than the working directory.

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