https://bugs.winehq.org/show_bug.cgi?id=42874
--- Comment #18 from Olivier F. R. Dierick o.dierick@piezo-forte.be --- I got a battle.net update during the last week and it managed to download and install two game updates afterwards, in Debian 8. I think the major change is dropping 32bit support completely.
So far, the issue seems to have been fixed by the app developers. Before resolving, I will wait a few days for another update, to be sure.