This has recently been brought up to date. Or rather, sport has been brought up to date: the entry for this word in the OED is one of the revisions which were made to the Dictionary on 11th September. (A few new words or meanings have also been added; you can see them here.)
The word sport has a different feel today than it had a hundred years ago. Sport was becoming 'organized' in the late nineteenth century. Before then, the term was largely used in the sense 'entertainment' (betraying its origins in 'disport') or in the narrow sense of hunting, shooting, and fishing. The semantic movement of the word over the centuries is demonstrated in the various senses it develops, but also in the evolution of phrases and compounds associated with its various meanings (early period: in sport, to make sport; 18th century: the sport of kings; modern period: sports clothes, sports centre, sports psychology, sport utility, etc.).
The entry for sport and its associated phrases, compounds and derivatives, together with the quotations, runs to over 19,000 words. For the benefit of those sad people who have no access to the OED Online I would have liked to have cut and pasted the entry here, but this would have made an over-long post. Anyway, the annual subscription is only $295; many institutions all over the world have it, or you could move to England where a (free) subscription to a public library will enable you to log on to it at home.
It has be said that many of its half-million entries do not make particularly engrossing reading. Under sport, for example, we can find a note about sportswomanship: The performance or practice of a sportswoman; skill in, or knowledge of, sport; conduct characteristic or worthy of a sportswoman. It includes a quotation from Tait's Magazine indicating that the first recorded use of the word was in 1833; all this is, I suppose, quite interesting, but not tremendously interesting and not really very useful to know.