Wikipedia, while not necessarily the end-all-be-all of knowledge and correctness
state that:
The closest to an international agreement on a definition is provided by SportAccord, which is the association for all the largest international sports federations [...], and is therefore the de facto representative of international sport.
SportAccord uses the following criteria, determining that a sport should:
* have an element of competition
* be in no way harmful to any living creature
* not rely on equipment provided by a single supplier
* not rely on any "luck" element specifically designed into the sport
They also recognise that sport can be primarily physical (such as rugby or athletics), primarily mind (such as chess or go), predominantly motorised (such as Formula 1 or powerboating), primarily co-ordination (such as billiard sports), or primarily animal-supported (such as equestrian sport).
There has been an increase in the application of the term "sport" to a wider set of non-physical challenges such as electronic sports, especially due to the large scale of participation and organised competition, but these are not widely recognised by mainstream sports organisations.
I bolded the bit relevant to computer games, the rest is kept mostly to stoke the fire for people not considering formula1, chess, and horse racing sports.
