No, the Cash Register System Act does not cover e-commerce. It follows from Section 2(a) of the Cash Register System Act that sales that take place via the internet or cash-on-delivery are not considered to be cash sales. The delimitation is of importance in cases where payment and delivery take place online simultaneously (e.g. payment for downloading services, software, etc.).
If the goods are ordered and paid for online, but collected from the store, the payment will be considered an advance payment which must be registered via the customer’s account (debt to the customer). If a sales receipt is to be printed from the cash register system when the customer collects the goods, it must be possible to reconcile this sale against the previous payment.
If the goods are ordered online, but collected and paid for in the store/restaurant, this will be counted as a cash sale which must be registered using a cash register system.