There is no "official" way for you to download it.

IIRC it is stored in your Google Drive under an API key that is dedicated to whatsapp (in some kind of per-app storage). I don't really know much about Google Drive API.

However, I am fairly sure that the key is in the binary on your phone, so it shouldn't be much of a challenge to get access.

I think there was something like this on Github once, that no longer works (due to trivial changes, likely).

Update: https://github.com/YuriCosta/WhatsApp-GD-Extractor-Multithre...

Looks recent, didn't try myself.