Whether any equipment needs to be earthed or not depends basically whether it is double insulated or has an isolated switched mode power supply.
Most if not all laptop computers will be safe to run on a 2pin plug.
It is the same with modern VCRs, televisions CD recorders etc.
On these equipments, a 3pin plug will often be fitted with a plastic Earth pin anyway.
The false earth pin is there to release the shutter device which guards against contact with the live pin on the socket.