Hi Capt and welcome to Android Forums!
The only thing I can think of is maybe there is some malware on your phone that is trying to install other apps. I would run a full scan with AVG anti-virus. If that app is not on Play, then that's cause for concern and a factory reset to get id of any nefarious software that might be on your phone.
It also might not actually be a download, but rather a push notification advertising it and offering to take you to the download page. Unwanted push notifications are an unpleasant reality.
Maybe someone else has another solution, but that's what I have for you
It's great to have you here!