What that means for people who passed the test before 1998 is - DO NOT throw your old paper license away, no matter which car rental employee tells you to do so. It is still valid, but, as the article explains, if you want to rent a car in the UK (and abroad) you'll need to apply for a code from the DVLA.
One more reason why, if you have an international license, or a license from another country (like a US license) it might be easier to use that when renting.