For installer help and issues see Blizzard App on AppDB
Everything--once you follow the steps in extra comments.
What does not
Without the steps in extra comments the Battle.net installer will finish successfully but once opened it will hang at "Loading account information..." (presumably because wininet is not installed yet).
Once wininet is installed you can successfully install Hearthstone from the Battle.net client but running Hearthstone will result in the error "Closed Failed to load asset PlayErrors32".
Once wininet is installed and msvcp100 has been added as a (native, builtin) library override everything works.
What was not tested
I wasn't able to cause an exception/crash so it may be that the dbghelp library override (to disabled) is still required for the bug reporting tool to function.
1. Install winetricks $ sudo apt-get install winetricks 2. Install wininet $ winetricks wininet OR via the GUI: winetricks -> Select the default wineprefix -> Install a Windows DLL or component -> wininet 3. Add msvcp100 override (native, builtin) GUI: winecfg -> Libraries -> New override for library (type in) msvcp100 -> Add The new entry should default to (native, buitin) but if not edit it and select (native, builtin).
|Operating system||Test date||Wine version||Installs?||Runs?||Used|
|Show||Ubuntu 16.04 "Xenial" amd64 (+ variants like Kubuntu)||Jan 07 2019||4.0-rc4||Yes||Yes||No||Platinum||M. O.|
|Show||Fedora 28 x86_64||Dec 07 2018||3.21||Yes||Yes||Yes||Gold||xsimplex|
|Show||Arch Linux x86_64||Jul 14 2018||3.12||Yes||Yes||Yes||Gold||Maciej Stanczew|
|Show||Fedora 28 x86_64||May 17 2018||3.8||Yes||Yes||Yes||Gold||Olof Sjodin|
|Show||Arch Linux x86_64||Apr 24 2018||3.5||Yes||Yes||Yes||Gold||Ozan|
|Bug #||Description||Status||Resolution||Other apps affected|
|23807||Unsupported texture formats: DF16, DF24, RAWZ: format unrecognized(909198916)||NEW||View|
|35291||setcap on wine-preloader causes application problems (Hearthstone)||NEW||View|
|38916||Hearthstone fails with 'GLOBAL_ERROR_ASSET_LOAD_FAILED' when using Wine from Ubuntu PPA (broken package?)||REOPENED||View|
|42845||Hearthstone crashes at loading screen||NEW||View|