In places like South America, Africa and Asia it was — and still is — fairly common to share devices with the whole family. Like in Brazil for a good period of time the computer would sit in the living room. It was an investment too big to stay in one person´s room — and parents would have more control over the contend coming from “that internet thing.”
MAYBE this was behind the first change from MY COMPUTER to just COMPUTER. THIS COMPUTER is a good solution because of the way we use them today and the proposal of Win10. Computers are just windows [pun intended] to an online server and online services. 
Good reflection, I will be more careful when tagging these things in the future.
Cheers!