It isn't free, but You could install ManicTime clients on each computer of the persons you need to track. The client can be used for free (commercially), if I remember correctly. But if you buy a license for each client, there is an option to not show the client in Windows, so the person wouldn't know this software was even there.
You can then install ManicTime Server on a server or your own computer, This one costs money (30 day trial). Then you can tell the clients to sent their reporting to your server and you will have your overview. You can see how long people are busy, at what times they work/play, etc. All in nice diagrams and such. These can be exported to different types of documents for easy presentation to you/your boss.
Network sniffers are usually intended for troubleshooting issues in a network, not for tracking what people are doing. Although such a thing can be done, the loads of data you'll need to filter from the content generated by a sniffer, takes quite some work and afterwards you still have a garbled mess of content to extract data from for your purposes. Software for Packet Inspection sounds more useful for that purpose.
ManicTime is much simpler to setup and gives you what you want in nice graphs. Don't think it is that expensive either and qualifies as a business expense (if they have such a thing where you live).