Would agree with this, you can be successful at a game purely if someone tells you exactly what to do, whereas in a sport there is some skill required in the 'doing'.In my book darts involves some physical demands - including steadyness, hand/eye co-ordination, muscle memory, control of breathing and muscles (sport) but chess and poker don't (games - although could argue 'control of emotions' I guess ).
Always exceptions though as, by that logic, playground games such as It/Tag/whatever-you-called-it would be a sport.
Darts is definitely a sport, though.