Just remember to put good host in configuration in Live Recorder object. It can't be just 'localhost', better put there ext IP or host, something which is accessible from other computers in network / internet.
And, one interesting thing: If I only add new VirtualHost in Apache httpd.conf with other PORT, say 8080, (and NO any changes to eZ settings), other computers can have the video played thru port 8080.
One more interesting thing: If I change the newly added virtualhost's port from 8080 to 8081, other computer CAN have the video played thru port 8081.