In the article, it says just that:
*On Wednesday, Asahi trialled using paper-based systems to process orders and deliveries in a small-scale trial and it is in the process of figuring out whether to proceed with more manual-style deliveries.*
It should be noted that with complex ERP (Enterprise Resource and Planning) systems combined with JIT (Just in Time) manufacturing means that not only taking of orders and the making of deliveries is disrupted, but the process of procuring beer precursors, this is from filtered water, barley, hops, yeast, rolls of raw aluminum to make cans, can tops etc, maintenance parts, cardboard boxes, etc.
The extent of the breach isn't fully known either. It's possible it compromised their o365 or google enterprise suite. meaning all their contacts, mobile device data, and whatever else is managed via mdm could all be ransomwared or completely deleted.
Any interruption can cause easily cause problems for days. Fortunately, shortages aren't immediate at the point of sale since large distributors like Lawsons, 7-11, etc, will have a large quantity available at distribution centers around the nation, it's just that they don't last forever.
Despite losing access to their data to the systems, they should be able to come back online with some limited capacity in weeks, in the meantime, distributors can juggle and rotate supply until newly manufactured beer starts showing up at loading docks.