ITS UNLIKELY that "Players" would have made its Kennedy Center bow last week if Center chairman Roger Stevens had not trailed along on his wife Christine's trip to Australia on behalf of whales.

Christine Stevens is secretary of the Society for Animal Protective Legislation, and her interests in the organization took her to Australia last fall. In that unlikely stop for American theater producer, Roger Stevens discovered "Players," written by Australian David Williamson.

Originally the drama, which opened Wednesday for a five-week run at the Eisenhower Theater, was titled "The Club". But because Eve Merriam's off-Broadway success has that title, the name was changed.

It was with something of a yawn that playwright Williamson heard through his agent that "some Yank wants to produce your play in America." At that point Williamson was filling a visiting professorship in Aarhuf, Denmark, where bleak winter can make a man, who has heard such offers before distrustful.

On the afternoon of July 14, just as Williamson was about to meet Stevens for the first time in his Kennedy Center office, a phone call for Williamson came through from Australia, where it was 2 in the morning.

It was Williamson's agent and, according to the playwright, he was "drunk as a fish. He'd had some drinks to stay up and track me down to report that 'Players' has just won the top award of the Australian Writers' Guild as best script in any medium."

Stevens was not surprised. "That's what I knew when I offered to produce the play here," said Stevens, who despite his 6-foot-2 frame has to look up to address Williamson.

Williamson is 6-feet-6 and looks 10 years younger than his age of 36. He was born in Melbourne as part of that generation, as he says, "brought up to be scientists." He seems to have taken to it readily enough to be a lecturer in thermodynamics at Melbourne's Swinbourne Institute of Technology, where he also taught psychology.

"Ever since a boy, though, I'd wanted to be a writer. Even when I was 4, I always enjoyed writing dialogue, creating school and university playlets, but I was very much aware that playwrights didn't earn livelihoods in Australia. Psychology seemed a natural substitute for my kind of writing, which I like to think is based on Psychological insights.

"In the past 10 years everything has changed. Of course I didn't know that Roger Stevens had been one of the American backers of a famous Australian play, "The Summer of the 17th Doll." Ray Lawlor's play had been a London hit, and that's the way Australians were heard from 20 years ago.

"That system's changed. Culturally, I think we Australians are closer to Americans than to the British. Now I'm not the only Australian earning a living writing plays, films and TV."

Williamson's first full-length play, "The Coming of Stork," had a swift success in 1970 at Sydney's Cafe La Mama, which led to his assignment to write its film version the next year. Two more plays, "The Removalists" and "Don's Party," established him as his country's most-admired young playwright. The former had performances off-Broadway and in Cleveland and Los Angeles several years ago.

"I'm lucky, considering the rivalry between our two major cities, Melbourne and Sydney, that I seem to have been discovered in Sydney, so both places accept me.

"Well, 'accept' - maybe that's a bit strong, too confident. La Mama, which introduced my first play, tends to view me, I suspect, as too commercially successful to be of much interest to them any more.

"That's a strange thing that happens when writers begin to appeal to the mass rather than just their initial cult. I don't understand it. Of course, how long I'll be commercially successful, who knows?

"In 'Players', as in much of what I write, I'm concerned with power, what it does, what it takes. I've used a popular, easily recognizable image, a football team and how management attempts to force a coach's resignation.

"Australian football is unlike any other, different from rugby, soccer and your gridiron play. We have 18 players to a team, there is strong physical contact and it's rough.

"Over recent years it's evolved from a gentlemen's club to a well-paid, big-public sport. The final attract crowds of 120,000. There may be a few phrases in the dialogue that won't be familiar to Americans but they're wholly unimportant.

"The main theme is power and the subsidiary one of change. I'm afraid I've made it all sound rather heavy, portentous, but that's not the way I write a play. I make every effort to be entertaining. I'm the last to condemn commercial theater. I believe in it. Getting a play and its subject matter before an audience is a good deal of what playwriting is about. I want to arrest audiences as I think all good playwights do."

Williamson and his wife Kristin, who writes for The Melbourne Age, welcome Washington's heat.Right after Australia's winter last year they went for a second one in Denmark, so they've had almost a year without sunshine. This unexpected side trip to America-their three sons, ages 12, 10 and 15 months, remained in England - is a welcome diversion. A bit delayed, Williamson will soon be back to his writing routine.

Playwrights should check future International meetings of animal protection societies. It's just possible that the husband of a delegate can be lured to a theater not normally visited by American theater producers.