I had the same problem on Linux. Reinstalling BattleNet in a different prefix, and symlinking the game to the new prefix helped. However, I still have the updating issues on the new prefix, so I’m not sure whether the problem is related.
The prefix giving me the error provides following errors in the log:
002c:err:wineboot:process_run_key Error running cmd L"C:\\windows\\system32\\winemenubuilder.exe -r" (2).
0128:err:module:map_image_into_view Could not map L"\\??\\C:\\Program Files (x86)\\Battle.net\\Battle.net.13747\\libcef.dll" section .reloc, file probably truncated
0128:err:module:import_dll Loading library libcef.dll (which is needed by L"C:\\Program Files (x86)\\Battle.net\\Battle.net.13747\\battle.net.dll") failed (error c000007b).