The CE marking is a kind of trade passport for the European marketplace: it allows the manufacturer to freely circulate their product throughout the 30 countries of the European Economic Area (EEA).
The great benefit for manufacturers is that there is now only one set of requirements and procedures to comply with in designing and manufacturing a product for the entire EEA. The various and conflicting national regulations are eliminated. As a result, the product no longer needs to be adapted to the specific requirements of the different member states of the EEA.
In addition, it may be considered a benefit that by implementing the requirements, the product will be safer for the user and this may also reduce damage and liability claims.
A competitors product carrys the CE marking yet I would class it under pharmaceutical (its an analgesic).
Can they really have the CE mark?
Pharmaceuticals typically do not require CE marking. Maybe there is an overlap with the Medical Devices Directive, but in principle there are clear divisions between regulations for pharmaceuticals and medical devices.