In my opinion, i would like to say poker player is both sportsman and gambler. An player called sportsman when they playing poker in tournament/event and an player called gambler when they playing poker in cash game(not event).
When a games turned into tournament is called a sports which is theres a contestant, price, thropy, official, event organizer, audiens, news, media, sponsor, etc. And everyone who participate have common goals to be a champions.
But how about cash game ? can you find the audiens ? sponsor? thropy for the winner ?. its called games for gambler. the common goal is for take $ from another players.