No. It is not a requirement.

However, bear in mind that VAT is payable on all shipments that are imported into South Africa.

This means that an importer will pay VAT but, if not VAT registered, will not be able to claim it back as input VAT. In order to maintain the same profits they will have to charge higher prices than their competitors.

And what about exporters? They, also, are under no obligation to be VAT registered. Whether they are, or not, their customers will not pay VAT, because exports are zero rated. But, as with importers, they will not be able to claim the Input VAT on their purchases. In order to maintain the same profits they will have to charge higher prices than their competitors.