Since when did "need" come into the use of dialect vocabulary? The thread is not about "offie", but I know that as well as I know "beer-off". Why "beer-off"? Because most of the 1930s to 1960s customers went there to buy beer - not yet having developed a taste for posh, expensive wine.there isn't really a need for another.
I seem to recall that early licences distinguished between Beer, Porter, Wines and Spirits - and whether they could be consumed on or off the premises. The licensee was required to clearly display details of the licence type above the door. In the area I know well, most would be licensed for beer only. You may have heard of it - a brown beverage with a large white foamy head 😂I'd never heard it either, before seeing this thread, and would have interpreted it in a way similar to play-off. That is, I'd have assumed it was some kind of beer-drinking contest (perhaps involving 'yards of ale').
If someone then told me it was a shop at which beer could be bought, I'd have assumed it to be a shop that specialised in beer and did not really sell much in the way of wines and spirits. After all, given that the term 'off-licence' already exists, there isn't really a need for another.
I'm surprised that sound shift did not know it: I'm also from Derby (north part of the city) and, to me, it is standard local English.In ... Loughborough ..., I very rapidly learnt beer-off. It's the absolutely standard term in that area, but I don't know how far it stretches across the East Midlands.