You ignored the "setting its own goals" part, which we haven't even started on yet. Humans define the arithmetic problems. Humans define what it means to win at chess and Go. Humans choose a specific destination to drive to.
Once humans have defined and programmed what do to, the machine happily does it much better than any human could (depending on the domain).
One day we'll be tempted to write a more serious, more complex "game", with real world consequences. For those, we'd better specify our goals precisely, lest we face unforeseen unfortunate consequences —there will be reasons why the machine does it better, ranging from faster computation, exquisite motor control, or a total lack of ethics —assuming ethics wasn't part of the programming.
Next thing you know, you need to solve the Friendly AI problem.
