Мне помогла эта инструкция, нужно отключить dbghelp.
Run winecfg. (If you have multiple prefixes, make sure it is the correct prefix) In the 'Libraries' tab, type dbghelp into the 'New override for library' box. Click 'Add', then 'Yes' when it asks if you are sure. Click on 'dbghelp' in the 'Existing_overrides' list. Click 'Edit'. Set to 'disabled'. Click 'OK', then 'OK'. Battle.net Client should now run.