NO, LabWatcher is installed on ONE computer in your network. The interface that LabWatcher is watching should be hooked to a Managed Switch and the Managed switch should be told to Mirror the Routers traffic to the Port labwatcher is hooked to. You can also get or make a Network TAP and hook it between the Router and Switch and monitor that. OR OLD School, if you have a OLD 100baseT HUB you can plug your router and labwatcher into that and monitor your network.
In Short, the interface you are watching should have all the internet traffic flowing across it. This will allow you to see all the traffic on your network.If you install it on a computer and do not have any of this setup, you will see that computers traffic, this can allow you to play and see what the program will do without having to do any configuration.
For example, at my house I have a netgear switch. The Router is plugged into port 1, the server(that has labwatcher on it) has 2 NICs and they are plugged into ports 2 and 3. In the Switch I have told it to mirror port 1 to port 2. In LabWatcher I told it to monitor the NIC that's plugged into port 2. Voila, I am watching the entire network.