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Of American-English origin, the phrase to have the game by the throat, and its variants, mean: to be in control of a situation; to be in a dominant position.

This phrase occurs, for example, in an account of the basketball match between the Louisville Cardinals and the Syracuse Orange that took place at Syracuse, New York, on Tuesday 14^th January 2025—account by Russ Brown, published in The News-Enterprise (Elizabethtown, Kentucky, USA) of Thursday 16^th January 2025 [page B2, column 5]:

The Cards dominated at both ends of the court from beginning to end. They grabbed the game by the throat with a devastating 3-point bombardment bridging the halves, hitting four straight triples during a 12-0 run for a 43-27 halftime lead 30 seconds into the second period, then expanding it to 21 by the first media timeout.

The phrase to have the game by the throat originally referred to hunting game animals.—Cf., below, quotations 1.1, 1.2 & 1.3.

It seems that this association with hunting was later lost, and that the phrase became associated with the sense rule-based competition of the noun game.—Cf., below, quotations 2.1, 2.2 & 2.3.

These are, in chronological order, the earliest occurrences of the phrase to have the game by the throat and variants that I have found:

1-: Literal use:

1.1-: From A Deer Hunt on the Vermillion, by “a boy thirteen years old”, published in The Ottawa Free Trader (Ottawa, Illinois, USA) of Saturday 30^th March 1867 [page 6, column 1]:

We saw that the gallant stag had baffled the well trained pack for the last time. He made a terrible plung [sic] through the hedge for his life, but the trackers were after him, thirsting for his blood. They gave him a slight chase for about a half mile, when the foremost of the pack, old Ranger, grappled his antlered game by the throat, throwing him on his haunches.

1.2-: From That Blamed Dog, published in The Sun (New York City, New York, USA) of Monday 4^th August 1873 [page 4, column 1]—reprinted from the Chicago Times:

Dick Slater is a Randolph street saloon keeper, and very proud of his skill with the rifle. He shot a lynx once, or claimed he did, and as lasting proof had the animal neatly stuffed and set up in one of his show windows. Four boys were passing the window on yesterday morning, and stopped to look at the lynx. One of the boys had a bull dog, and the bull dog stopped also. No sooner did he get his eyes on that lynx, however, than crash he went through the window, seized the game by the throat, and shook the stuffing out of it in less than no time.

1.3-: From The Daily Telegraph (Saint John, New Brunswick, Canada) of Wednesday 31^st August 1881 [page 2, column 4]:

A Good Bear Story comes from Danforth, and was told to us by a man who saw the bear. Last spring Mr. John Russell of that town saw a bear, apparently about six months old, engaged on the margin of a frog pond making his breakfast upon the amphibious reptiles with which the locality abounded. As soon as bruin saw his adversary, he made tracks towards the adjacent woods, hotly pursued by Mr. Russell, who soon overtook him, brought him to bay, and then came “the tug of war.” Having no weapon except what nature had provided, he was obliged to try titles with muscle vs. muscle. In less time than it takes to write the facts, he had his game by the throat, and succeeded in stopping the breath until the predatory brute lay limp and apparently defunct. Presuming life to be extinct, he dragged the body home and left it in the door-yard. Imagine the victor’s surprise when, half an hour afterwards, he returned to take the hide off, and found bruin recovering from his recent indisposition and ready for business. He was soon transferred to close quarters, and is at present an object of interest to guests of the village hotel.—Aroostook Pioneer.

2-: Figurative use:

2.1-: From The Buffalo Enquirer (Buffalo, New York, USA) of Monday 21^st August 1899 [page 4, column 6]:

NEW LEAGUE IS AN ASSURED GO.
Cincinnati Sporting Writer Champions the Cause and Welcomes a New Organization.

One would infer from the remarks made by some of the magnates on the subject of the new league that no other organization than the National League and the American Association of Base Ball Clubs has a right to exist—that the life and future of the game lies entirely with the gentlemen who now have the national game by the throat and that any man or body of men who dare to start in opposition to the existing organization are usurpers and not worthy of the consideration of the general public, writes Charles Zuber in the Cincinnati Times-Star.

2.2-: From Will They Bow to Freedman?, a correspondence by Joseph Vila from New York City, dated Saturday 27^th October 1900, published in The Courier-Journal (Louisville, Kentucky, USA) of Sunday 28^th October 1900 [page 10, column 1]—the following is from an interview of Ned Hanlon (1857-1937), who managed the Brooklyn baseball team from 1899 to 1905:

“I know very well what is the matter with baseball in Greater New York. The newspapers have the game by the throat, and you can not blame them. Other sports are being boomed to such an extent that the public has temporarily lost interest in the national game. The newspapers have not been treated with proper courtesy. Baseball depends upon the press for free advertising such as no other public entertainment enjoys. The newspapers can make or break anything in the way of sport. During the past season I noticed that columns were devoted to prize-fighting, horse-racing, and golf, where baseball got only a few lines. It is also a fact that reporters who used to cover ball games for good salaries were taken away from the games, and in many instances office boys were substituted. It makes no difference whether you have a champion team or not: if the newspapers do not notice it and do not keep it conspicuously before the public in big type there is bound to be a lack of interest. If the Brooklyn Club this year had received the amount of space devoted to prize-fighting the grounds would have been packed every day. This is the keynote to the sitnation [sic]. Look at the papers in any other League city and you will find that baseball receives the preference over all other sports, while in Greater New York it is the under dog. From my way of thinking, the New York papers have concluded that free advertising doesn’t pay when there is a willful attempt to kill the game going on here.”

2.3-: From Little Miss Millions or, The Witch of Monte Carlo. A Romance of the Riviera, by the U.S. novelist St. George Henry Rathborne (1854-1938), published in the Butler County Press (David City, Nebraska, USA) of Wednesday 2^nd July 1902 [chapter 11, page 8, column 2]—the following takes place in the Casino de Monte-Carlo, in the Principality of Monaco, on the French Riviera:

Realizing that they were up against the very toughest argument that had ever fallen upon Monte Carlo, the dealers were not at all anxious to continue playing indefinitely.
The sooner they admitted the grave fact that a third time the famous bank must cry quits, the better for them.
Merrick had done well.
Not a single slip or mistake had been made. There was but a unanimous opinion among the nerve-racked spectators that these two men really held the game by the throat.