Mark Penn, who most recently received a certain amount of infamy as Hillary Clinton's chief strategist--perhaps the non-Clinton most responsible for her primary loss--pointed to a particularly odd poll result¹ from 2006 in his most recent book. In a poll of 601 young Californians asking what they'd be doing 10 years from now, amongst the answers such as "a lawyer," "a nurse," "an astronaut," one percent of respondents said they'd be "a sniper." (Ezra Klein, my
primary source in this article, mentions that the study had a margin of error of plus-or-minus four percent, so take this result with a grain of salt). Penn bases an entire chapter of his book
Microtrends on this result, claiming that this demonstrates a "new patriotism," and a desire “to master complex mathematical formulas like how distance or wind might affect the path of the bullet.”
¹He is also responsible for the inane nickname "Soccer moms."
By this point, it should be clear that Mark Penn is not someone who's analysis should be trusted. You don't need to know a lot to know that kids are interested in snipers not because they're fond of math, but because snipers in video games are cool. You don't need to calculate integrals in a video game to blow someone's head off. In most video games, shooting someone with a sniper rifle is literally instant death: the bullet gets there faster than light and drops the target wherever it hits. In fact, an argument could be made that the appeal of snipers reflects a certain cowardice on the behalf of American youth: they want to be able to beat their enemy without ever being directly confronted and with almost no danger themselves.
Snipers have had a bad run in American cinema. For decades, the most well-known sniper movie was the Sniper series, staring Tom Berenger, shortly after he was catapulted to mid-range stardom in Major League. These are not good movies. To the best of my knowledge, the best sniper movie is Enemy at the Gates, which is not a particularly good movie. Shooter, staring Mark Walberg, was another recent attempt at the genre, though was pretty much a flop. There's also Jarhead, which is certainly the most realistic sniper movie I've seen (based on a true story, though a less exciting true story than Enemy at the Gates), though one with no actual headshots. The most sympathetic sniper in film is almost definitely Barry Pepper's Private Jackson in Saving Private Ryan, but he's a walking war movie cliche: the devoutly religious gunman.
The popularity of snipers must largely be from video games--movies have dropped the ball on this entirely.
Snipers might also be popular from, well, real life. The History Channel has a cottage industry around sniper stories. By law, half of the History Channel's shows have to feature World War 2; by luck, some of the best sniper stories come out of that war. My personal favorite is the story of Simo Häyhä, a Finnish soldier from the Winter War--where the Soviet Union invaded Finland, thinking it would be a pushover. Finland had already revealed itself to be a little badass of a country. The Soviets invaded during the winter--significant portions of their paratroopers were killed off when they landed in 10 feet of snow--farmers would go out, find the holes, fire a shotgun down the hole at the trapped paratrooper, and move onto the next hole.
Out of this war came Simo Häyhä, a hunter and farmer who did all of his sniping with the plain sights on his rifle (he believed that using a telescopic sight would force you to raise your head higher, making you an easier target to find). During the winter war, where temperatures hovered between 0 and -40 degrees, he killed 505 Soviet soldiers with his rifle, over the course of 100 days. Those are the confirmed sniper kills. He had another 40 unconfirmed sniper kills. He also killed close to 200 men with a submachine gun. He was eventually shot in the face. Even though he was injured, he managed to kill his attacker and return to a hospital. He recovered, and died in 2002 at the age of 96, over 50 years after the end of the Winter War.
I don't have any point beyond that. Snipers can be pretty awesome, sometimes.