I've discovered that setting it to OFF breaks a great deal of HeidiSQL's features: table editor, data tab... I'd say that the column parser does not recognise unquoted identifiers. I'm not sure if it's a known issue (a ticket search for "sql_quote_show_create" doesn't return results).
It can be disabled from the "Host/Variables" tab or by running:
SET @@session.sql_quote_show_create = 'OFF';