Would You Rather

Iris, a young woman caring for her sick brother Raleigh, is unable to afford his treatment costs. Her brother's oncologist, Dr. Barden, introduces Iris to Shepard Lambrick, a philanthropist, who offers her a deal: if she wins a parlor game at a dinner party, his charitable foundation will pay for Raleigh's leukemia treatment and locate a bone marrow donor for him immediately. Dr. Barden was a former winner of the game. Iris reluctantly accepts.
The next day at Lambrick's manor, Iris is introduced to his son Julian and the other contestants: Lucas; Travis, a war veteran; Linda, an elderly, paralyzed woman; Peter, a gambling addict; Cal; Amy; and Conway, an alcoholic debtor. A steak and fois gras dinner is served but, Iris, a vegetarian, initially declines to eat it. Shepherd then offers her $10,000 to compromise her principles, and so she eats the steak. When Shepard realizes Conway is a recovering alcoholic, he offers Conway $10,000 to drink a glass of wine. When Conway declines he then offers him $50,000 to drink an entire decanter of Scotch. Conway accepts the $50,000 and reluctantly drinks the Scotch.
After dinner ends, the game begins. Shepard reveals it to be a version of the party game "Would you rather...?", in which players must choose between two options. Shepard gives his guests the opportunity to leave without playing, but everyone stays. After Shepard's butler, a former MI5 agent named Bevans, wheels in an electric shock machine, the drunken Conway attempts to leave but is shot dead. Each contestant is then forced to choose between shocking themselves or another person. Each player has 15 seconds to make their choice. Iris, Cal and Lucas (after nodding his consent to Travis) shock themselves. All survive, and nobody is eliminated.
In the second round, each contestant must choose between stabbing someone in the thigh with an ice pick or whipping Travis three times with a sjambok. Travis is singled out after insulting Julian in the previous round. In the second round the players are given 30 seconds to make their choice. Travis submits to being whipped by Iris and Lucas to save anyone from being stabbed. On his turn, Travis must choose between being whipped by Bevans or stabbing Lucas; he chooses to be whipped again. Knowing Travis will not survive another whipping, Peter stabs and accidentally kills Linda when he hits her femoral artery. Shepard gives Amy the choice to stab anyone, and she chooses Iris, having reasoned that she must kill the other players to survive and win the game. Cal agrees with Amy and chooses to whip Travis, who is eliminated when he becomes unresponsive.
Lucas causes a distraction, and everyone but Amy attempts to escape the room. Cal advances on Shepard with the sjambok as Lucas attacks the guards and Iris escapes. After Shepard shoots and kills Cal, the others surrender. Shepard sends Bevans and Julian after Iris. Julian finds Iris first and attempts to rape her, but she stabs him with the ice pick. Dr. Barden, who has had second thoughts about sending Iris to Shepard, breaks into the mansion to save her. Drawn by her cries, Barden and Bevans converge on her. Bevans kills Barden, escorts Iris back to the game, and sends Julian upstairs.
After Shepard apologizes to Iris for Julian's behavior, the third round begins: a choice between getting dunked in a barrel for two minutes or an unknown task written on a card sealed until after the player chooses. Peter chooses his card, which holds a symbol representing what Shepard states to be lighting a firecracker in Peter's hand, but when the firecracker is presented it turns out to be a quarter stick of dynamite. Shepard has Bevans secure the stick in place with duct tape, and Peter is forced to light it, given false hope that it may be a dud. The shock causes a heart attack, and he dies. Lucas' card forces him to slit open his own eye. Iris chooses the barrel and survives; her card is revealed to have been extraction of all of her teeth. Amy, whose child died of drowning, chooses her card, only to find a barrel and a 4, representing the number of minutes she will be submerged, which coincides with the length of time without oxygen at which brain damage begins. Amy drowns.
Only Iris and Lucas remain for the fourth round. Iris wins a coin toss to go first. She is given the choice to either shoot Lucas to win the game, or spare him which would result in both walking away empty-handed. As Lucas attempts to talk her into sparing him and explains the struggles of his family, she abruptly shoots and kills him. Shepard crowns her the champion, gives her a bag full of money, and explains that a donor has already been located for her brother and he will have surgery later that week. At home, Iris finds Raleigh asleep on his bed so she heads to shower the blood off her. The next morning she goes to her brother's room only to find Raleigh was not sleeping, but had committed suicide by overdosing on his medication. Everything she had endured and done (including murder), had all been for nothing. Iris cries out in anguish.

Question: How does Conway die?
Answer: He is shot.