Family LTR permit refused, wife has to leave, can she come back on a tourist visa?

Your wife was (apparently) living in the UK with a perilous immigration status and has been given the standard removal instructions when the pathways for in-country appeals have been exhausted.

Can she fly back to South Africa and then apply for a visitor visa to come back while we sell the business and plan to move back to SA?

Yes, anyone can apply for a visitor visa. The sole condition is that the applicant must be outside of the UK and Islands at the time of their application (Paragraph 28).

From a practical point of view, when someone makes an in-country leave-to-remain application that fails and subsequent appeals fail, it is taken that the person has committed themselves to living permanently in the UK. This assumption has a profoundly damaging affect on the person's credibility as a visitor.

Moreover, the premise of liquidating a business is unlikely to be acceptable to UKVI because of her history of not understanding the rules or conditions of her visa. It's been clarified in comments that your wife entered on a spouse visa and was unable to further qualify because of the income hurdles (GBP 18,600 per year) in Appendix FM. There is no prohibition for an individual on a spouse visa to participate in the ownership of a business and it's not clear at all that the emotive article printed in Torquay Herald Express was authored by someone with a credible understanding of the rules. You would be better off relying on professional counsel.

Personal note: a long time ago when I was training, Keith Best told me that you cannot shame the Home Office because the Home Office has no shame, so it's likely they will follow through on your wife's removal.

Currently, South Africa is a visa-national country so a visa is required prior to departing for the UK.

In addition to being able to apply as a visitor, your wife also has the option to continue her human rights appeals from South Africa.