It was June 8, 1985, a date that still resonates in British boxing lore. McCloskey can't remember it, but he understands the impact McGuigan's stirring victory over Panamanian legend Eusebio Pedroza had on his homeland.
McGuigan, who had become a political peacemaker in the ring, returned to scenes of celebration on both sides of the Irish border after capturing the WBA featherweight title with a 15-round decision in front of an open-air crowd of nearly 26,000 at Loftus Road Stadium, west London.
McCloskey dreams of similar adulation after his HBO debut against England's Amir Khan at the MEN Arena, Manchester, on Saturday. "Beating Khan would probably surpass that," predicts the 31-year-old southpaw. "I'm fighting one of the most famous, recognized fighters. He's so hyped up. He's got celebrity status and such a high profile. Beating him would be a massive achievement.
"When you're in this game, you want to be the best and be successful - and follow in the footsteps of your local heroes. Barry was one of them. It would be an honour to come back from Manchester, get off a plane and be greeted by thousands of people. It would be amazing."
Most neutrals believe McCloskey's dream will remain in his head. He is a 6-1 outsider to relieve Khan of the WBA super lightweight title, even though he is unbeaten and the reigning European champion.
If he does fail, it won't be for lack of preparation. McCloskey, 22-0 (12), has been training in Belfast, about 50 miles outside his hometown, Dungiven, for nearly 10 weeks, seeing his young family at weekends.
"You always hear the old stories about fighters going away and leaving their families. I don't need to do that," insists McCloskey. "I like to see my kids. Having the kids there just makes me happy. If I'm happy, that can only be good for me."
McCloskey might need all the good he can get. Saturday's fight is seen as little more than a homecoming party for Khan before he heads back to Las Vegas for a mooted unification clash with rival champion Timothy Bradley on July 23.
But McCloskey, the WBA's fourth-ranked challenger, says he has a better chance than the oddsmakers are giving him. "If you look at the way I fight, and you look at the way Amir fights, I'm not as big an underdog as people think," reasons McCloskey. "For me, it's about victory. The way I fight, there's no doubt I can beat anybody.
"Amir's got so much speed and skill, but he's got flaws, too. He showed those flaws in the last couple of fights. He's very still, very square on, no head movement whatsoever."
"My elusiveness, my speed and my lateral movement can give anybody nightmares. Anybody who shares the ring with me doesn't enjoy it. People call me awkward. I say it's skill. I've got a good brain in there and I know what I'm doing.
"Amir's got so much speed and skill, but he's got flaws, too. He showed those flaws in the last couple of fights. He's very still, very square on, no head movement whatsoever.
"I was surprised how often [Marcos] Maidana caught him and he was so close to being stopped in that fight. He's very dangerous early on, but sometimes when a fight goes on, he can taper off a bit.
"I've been working with a conditioner for this fight and I'm in the best condition I've ever been in. I've trained for 12 hard rounds, so whatever comes my way on April 16, I'll be ready for it."
He will have to be. Khan, who won an Olympic silver medal aged 17 in 2004, has re-invented himself after his shocking 54-second knockout loss to Colombian Breidis Prescott nearly three years ago, and he is now hovering just below boxing's superstar bracket.
"I have to take my hat off to him," concedes McCloskey. "But he was looked after well and he was very well matched. How many people get knocked out and, within three fights, get a world title shot? He's a product of the business, to be fair about it.
"I do respect him as a fighter, but I don't think he's as good as they're making him out to be. He's not in the league of Manny Pacquiao or Floyd Mayweather. He's talking about moving from 140 up to 147. There are 147 fighters out there at the moment who would wipe the floor with him.
"Sometimes you can talk too much. You're better just staying focused on what's ahead of you. By talking about the other stuff, he's taking his eye off the ball with me."
By his own admission, McCloskey's career has been "very low-key," with a 10-round decision over former WBC lightweight champion Cesar Bazan in March 2008 making the only standout result on his record.
But McCloskey declares with a sense of destiny: "This is my time to announce my arrival on the world scene. I want to make my own history. People in America obviously don't know who I am, so they're probably expecting an easy fight for Khan. But they'll see what I'm all about."