RE:RE:SupplyChina is important for zinc in several ways. They are the major user of zinc due to their huge steel production capacity and production of galvinized products AND they do have zinc mines that seem to have increased output and may offset the worldwide supply deficit.
However you need to look at the total picture. LME inventories have dropped from 760,000 tons to 435,000 tons in the last year or a reduction of 325,000 tons. The Shanghai numbers you show illustrate a rise of 50,000 tons in the past year. The combined totals still show a dramatic drop in inventory and the two big zinc mines shutting down this year will add to the drop in inventory.
China has been cracking down on small mining operations to improve safety, reduce pollution and consolidate overbuilt industries. I doubt the small miners in China are going to offset this big worldwide trends. Guess we'll find out as 2015-6 unfolds.