1) "I play sport."
2) "I play a sport."
3) "I play sports."
In 1), 'sport' is a non-quantifiable noun, which takes no article. This is a general reference to 'sport' as an activity - you might say "Sport is good for you", but you would be unlikely to say "Sports are good for you", because 'sports' is always the quantifiable form of the noun.
In 2) and 3), 'sport' is a quantifiable noun (singular in 2) and plural in 3) of course) that refers to a particular sport, or particular sports.
Note also that 'sport' may be both an intransitive and a transitive verb:
1) "Do you sport with me, sir?"
2) "My car sports a fine set of wheels."