Translation:The CEO does not have a partnership.
According to the oxford german dictionary it translates to managing director or manager of a shop/restaurant or such like. Parnerschaft is definitely a partnership in the business sense. And I think in this situation it means "partnership in the business" - in other words you can be a managing directer without being a partner in, for example, a law firm. Or it could mean that he is the managing director of a company which is not a parnership (a legal term meaning the company has no legal identity and the partners can all be sued for any wrongdoing by the business), for example a limited company. At least that's my guess.
Geschäft=business führer=leader. Der Geschäftsmann=businessman. It appears the internet consensus is Managing Director (Wiktionary, Google Translate, Vocabulix) one site said CEO. According to Wikipedia Managing Director is synonymous with CEO. So literally it is the leader of the business.