As CBS2's Natalie Duddridge reported Monday, the victim was a U.S. Marine who recently graduated from The Citadel and was visiting the city from upstate.
The shooting happened around 5:15 p.m. near the Minskoff Theater at West 45th Street and Seventh Avenue.
"We heard the shooting and then I see a lot of people was running on this side. So they come over here like, 'There's a shooting over there! There's a shooting there!'" street vendor Aslam Chaudhary told CBS2's Ali Bauman.
Sources told Bauman investigators are working under the theory the shooting began as an argument between two groups of unlicensed vendors or street performers.
Police said the suspect was aiming for someone in a group of six men, but a bullet ricocheted and hit 21-year-old Samuel Poulin instead.
Poulin was taken to Bellevue Hospital with non-life-threatening injuries.
"The Citadel family -- in Charleston, South Carolina and around the world -- is greatly saddened to learn about what happened to our Class of 2021 graduate, 2nd Lt. Samuel Poulin in Times Square on Sunday when he was hit by a bullet from a shooting event unrelated to him. We are encouraged that he is reported to be in stable condition are sending our prayers and our love to his new wife and his family," Citadel President Gen. Glenn M. Walters said in a statement Monday.
Walters said Poulin holds a Bachelor's degree in physics, was a President's List cadet and "exemplifies the kind of principled leader The Citadel strives to produce."
Some people who work in the area said Times Square has been overrun with crime and violence is happening too frequently.
"We want tourists to start coming, you know? So if people hear things like this, they get scared," Chaudhary said.
Theresa Harrington is a longtime vendor in Times Square.
"You got a lot of newcomers coming out here and we don't know who's who," Harrington said. "You got somebody from Harlem. You got somebody from Brooklyn. Brooklyn, Harlem, Bronx selling the same things. C'mon, there's gonna be collisions somewhere."
Bauman also spoke to Zoi Levine, who was visiting from Ohio.
"We had an incident yesterday when a guy was just angry after we wouldn't give him money," Levine said. "So now, if somebody asks, I would rather just go ahead even if I don't have the money or don't want to."
Last month, three innocent bystanders were hit by stray bullets a block away from Sunday's crime scene. Among those injured were a 4-year-old girl and a tourist.
Watch: Mayor, NYPD Announce Safety Action Plan For Times Square
"Times Square Safety Action Plan to make sure that anyone who goes to Times Square knows they're safe and they're going to see plenty of police presence in Times Square," the mayor said.
"How can New Yorkers or tourists or anyone really feel safe when you announce these plans, but then we're still seeing unintended targets, innocent bystanders get shot in the middle of the day?" CBS2's Kiran Dhillon asked the mayor.
"Kiran, this is just how we change any situation we see," de Blasio responded.
NYPD Chief of Department Rodney Harrison expanded on the surge, saying, "The different strategy going forward is now we are going to be engaging these individuals that are selling or panhandling these CDs."
But many people who visit and work in Times Square said that's not enough.
"All they do is give you lip service and you get no action. I see one cop car in three blocks right now and that's ridiculous," Raj Samra said.
"We have to go back to a serious police forces now in New York City so that New York comes back to what it was before," added Yves Michiels, owner of BXL Cafe.
Meanwhile, police are asking anyone with information about Sunday's shooting to call them.
As for Poulin, he was taken to Bellevue Hospital in stable condition. He was recently married and his family said it is grateful he wasn't more seriously wounded.
CBS2's Ali Bauman and Kiran Dhillon contributed to this report.
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