In the session running pulseaudio in the machine that has a sound board (in this example, it has IP address 192.168.0.25), run the following command to accept audio from the network 192.168.0.0/24:
$ pactl load-module module-native-protocol-tcp 'auth-ip-acl=127.0.0.1;192.168.0.0/24' auth-anonymous=1
In the client session that run the program, export the PULSE_SERVER address, like this:
$ PULSE_SERVER=192.168.0.25 chromium &