The phrase "a game at which" is correct and usable in written English.
It can be used to describe a specific type of game or activity where certain skills or actions are performed.
Example: "Chess is a game at which strategic thinking and foresight are essential for success."
Alternatives: "a game in which" or "a game where".
It is a game at which addicts play even when the tokens are utterly mediocre.
A journalist from The Independent attended a game at which one of the pair, Zaur Sadayev, was booed by some Beitar supporters every time he touched the ball.
If in company, I mention the name of a famous friend or acquaintance, dead or living, I know that I may be an involuntary player in a game at which someone present is scoring marks against me.
What I did not understand then was how golf - with its arcane rules, codes of behaviour and etiquette - perhaps more than any other game, can reveal moral character, especially when you consider that it is a game at which it is so easy to cheat: a little nudge of the ball here, a mulligan there.
He could no longer play the graceful, detached game of the successful queer writer, a game at which Vidal and so many like him (Somerset Maugham and Tennessee Williams among them) was a master.
Football, a game at which all but three or four teams are consistently awful, is the last thing the tired, resigned, miserable majority of men on this planet have in common with each other.
A brief list: Middleton's A Game at Chess (which I did once see students perform); Schiller's William Tell; and, from the 20th century, JB Priestley's Johnson Over Jordan, Emlyn Wiliams's Spring 1600, Graham Greene's The Living Room.
But Nytra will not be able to do much to alleviate the fact that, apart from a few shining exceptions, this is not a Games at which Germany will be remembered for its stunning triumphs.
I don't remember who won, and I have yet to attend a game at Nationals Park, which opened in 2008.
The Orioles desperately want a game at Camden Yards, which last hosted a postseason game in the 1997 American League Championship Series, when Jim Thome's Cleveland Indians won the pennant.
He had not coached a game at Stanford, which was coming off a 1-11 season in 2006 and had not finished with a winning record since 2001.
