Offhand, I can't think of anywhere else in the world that implements this strict of a requirement. However, some existing POS systems may implement this sort of encryption depending on what the definition of "control unit" is and where the differentiation between "control unit" and "cash register" lies.
The reason I say this is because many POS systems (at least the ones that I've worked with) are essentially a bunch of dumb terminals that are networked to a central database and transaction processing server. No data is actually stored in the cash register itself, so there is only a need to encrypt it on the server side (and over the wire, but I'm assuming a secure network protocol is being used). You would need to get a lawyer to interpret what exactly constitutes a "control unit", but if this can be defined as something on the server side (in a networked POS case like this) then the necessary complexity to implement such a system would not be too onerous.
The difficult case would be where each individual cash register requires a unique encryption key, whether to encrypt data to be stored inside the register itself or to encrypt data before sending it to a central server. This would require a modification or replacement of each cash register, which could indeed prove costly depending on the size of the business and the age of the existing equipment. In many countries (the US in particular), mandating such an extensive and costly change would likely have to be either accompanied by a bill providing funds to businesses (to help pay for the equipment conversion) or written in a manner more like "all Point-Of-Sale equipment manufactured or sold after {{{some future date}}} must implement the following features:". Implementing rules that place expensive burdens on businesses is a good way for politicians to lose a lot of support, so it's not likely that a rule like this will get implemented over a short period of time without some kind of assistance being offered.
The possibly interesting case would be the "old-fashioned" style of cash registers which essentially consist of a cash drawer, calculator, and receipt printer and store no data whatsoever. This law may require such systems to start recording transaction information (ask your lawyer). Related would be the case where transactions are rung up by hand, written on a paper ticket (like is commonly done in some restaurants and small stores in the US). I often find it amusing how legislation focuses on such security for high-tech systems but leaves the "analog" systems unchanged and wide open for problems. Then again, Sweden may not be using older systems like this anymore.
I'm not sure exactly what US law requires in terms of encrypted records, but I do know that certain levels of security are required by many non-government entities. For example, if a business wants to accept credit card payments, then the credit card company will require them to follow certain security and encryption guidelines when handling and submitting credit card payment information. This is in part dictated by the local rules of legal liability. If a transaction record gets tampered with, lost, or hijacked by a third party the security of the transaction and record-keeping systems will be investigated. If the business did not make a reasonable effort to keep the data secure and verified, then the business may be held at fault (or possibly the equipment manufacturer) for the security breach which can lead to large losses through lawsuits. Because of this, companies tend to voluntarily secure their systems in order to reduce the incidence of security breaches and to limit their legal liability should such a breach happen.
Since device manufacturers can sell their equipment internationally, equipment complying with these Swedish restrictions will likely end up being used in other places as well over time. If the system ends up being successful, other businesses will probably volunteer to use such an encrypted system, even in the absence of legislation forcing them to do so. I compare it to the RoHS rules that the EU passed several years ago. Many countries that did not sign the RoHS legislation now manufacture and use RoHS-certified materials, not because of a legal mandate but because they are available.
Edit: I just read this in the linked article:
Certified control unit
A certified control unit must be
connected to a cash register. The
control unit must read registrations
made by the cash register.
To me, this sounds like the certified control unit attaches to the register but is not necessarily connected to it (or necessarily unique to a register). This definition alone doesn't (to my non-lawyer ears) sound like it prohibits existing cash registers from being connected over a network to a certified control unit on the server side. If so, this might be as simple as installing some additional software (and possibly a peripheral device) on the server side. The details link may clarify this, but it's not in English so I'm not sure what it says.