WhatsApp cofounder Brian Acton stated in 2015 that there would not be a WhatsApp API for developers. (WhatsApp cofounder: Sorry developers, no API for you). In the absence of an API, it comes as no surprise if there is not a convenient connector to pull data into Tableau.
Also, I'm given to understand that most WhatsApp activity is pushed down to devices, with very little cloud storage for conversations. I'm not sure if this applies to groups as well, but it could also explain the scarcity of cloud-based analytics.
On the other hand, you may be able to retrieve information from the WhatsApp data on your device and bring those into Tableau for analysis. This article (WhatsApp Group Chat Analytics using Excel and Power Query - Efficiency 365 ) discusses how to do this for Excel. Most of the article is devoted to cleanup that has to happen in Excel; you will probably find that much of that cleanup can be handled by Tableau, hopefully obviating the need for an extra ETL step.
At the end of the day, it looks like it's going to be a manual import of snapshot data. No options for a live connector that I can see. I may be wrong, though.
Hope this helps.
Thanks a lot for your reply and generous help. I will try the options you suggested.