I remember something like this in Oman as well, back when I lived there in the late 80s/early 90s.
Looking at the situation now though, it looks like it might be a very tiny bit more liberal, in that you still need a "personal consumption licence", but the quota appears to have been done away with.
https://www.angloinfo.com/how-to/qatar/lifestyle/food-drink/...
EDIT: yes article mentions this
The letter must be addressed to the Qatar Distribution Company, be stamped and signed by an authorised person within the company, and include the following information: