Starting with version 2.0.1 Blizzard switched from using the old launcher to a new one called "Battle.net Desktop App". The new one will crash but there is a fix.
The easy way
Use the crosstie to install the Battle.net Desktop App in the same bottle where the game was previously installed.
The hard way
Create a file called d3_tweaks.reg and copy&paste the following into it:
REGEDIT4
[HKEY_CURRENT_USER\Software\Wine\DllOverrides]
"dbghelp"=""
[HKEY_CURRENT_USER\Software\Wine\AppDefaults\Diablo III Launcher.exe\DllOverrides]
"dbghelp"="native,builtin"
[HKEY_CURRENT_USER\Software\Wine\AppDefaults\Diablo III.exe\DllOverrides]
"dbghelp"="native,builtin"
Use the registry editor to import the file. Click the link below for info on how to access it. Make sure to select the bottle where D3 is installed