SpongeBob it is not. The Korean dystopian drama depicts the killing of adults who compete in children’s games. The first episode culminates in a spray of blood and bullets as guns mow down competitors in a grisly game of red light, green light. Netflix rates it MA for mature audiences and said the series is its most-watched show within a 28-day launch.

It is generating buzz among kids, too, who hear about it from older siblings, on the playground, in memes on social media or through gaming platforms. Parents say their kids are coming home begging to watch it, or trying to sneak in episodes on their own. Some kids want to dress as the show’s characters for Halloween.

Common Sense Media, a nonprofit that rates shows and other content to help parents assess age-appropriate viewing, said its review for “Squid Game” is its most-viewed of any show in a one-month period. “Parents want to know what is ‘Squid Game’, what is going on with ‘Squid Game’,” said Polly Conway, senior TV editor for Common Sense Media.

The site rated it appropriate only for children ages 16 and older. “Parents need to know that the level of violence is very intense in ‘Squid Game’,” it advises.

Scores of commenters on Common Sense’s site have offered their own opinions.

“Those who say it’s fine for kids 13 and up must have very hardy 13 year olds,” wrote one commenter. Another provided an episode-by-episode guide to “squeamish” scenes to skip: “A bunch more contestants get shot in the head,” it advised for Episode 3. “It’s pretty good, just depends if ur mature or not,” wrote a commenter identified as a 12-year-old.

The children’s games featured in the show’s plotline, striking visual elements that lend themselves to Internet memes—including a giant robot-like doll—and parodies shared on social media are part of what draw kids in, pop culture and parenting analysts say. And kids have gotten so used to watching content on phones during the pandemic that some parents say trying to block “Squid Game” entirely is a losing battle.

Ms. Bilicki, who lives in Milwaukee, watched 15 minutes of the first episode and decided it was OK for her son, Troy, to watch. She reasoned that he already plays “Fortnite” and has seen horror movies, including 1981’s “An American Werewolf in London,” which she remembers being terrified by herself as a teenager.

“He was bored with it,” she said. “He knows how scenes are constructed. He knows what is fake and it doesn’t faze him at all.”

Sixth-grader Troy, who got his own phone last year, said he first heard of the show from YouTubers who watch and react to memes related to the show. He watched all 9 episodes from his phone in three days. He said he has also played “Squid Game”-related games on Roblox, a gaming platform popular with kids.

“You can actually experience what it was like in ‘Squid Game’,” he said. “It was really cool.”

Roblox said its safety standards don’t allow content that contains “extreme violence or serious physical or psychological abuse,” and that its moderators can address any inappropriate content within minutes.

In an emailed statement, a Netflix spokesperson said that “Squid Game” is intended for mature audiences, which means it may not be suitable for ages 17 and under. “We offer parents a wide variety of parental controls to make the appropriate choices for their families,” the statement added.

Some parents figure their kids are going to find a way to watch, and would rather they did so with parents. While watching season 2 of “House of Cards” with her 13-year-old son Ryan several weeks ago, Rachael Leventhal said he asked to watch “Squid Game” instead.

She wasn’t aware that it contained graphic scenes and violence, but went along with it. “I figured we are watching it together. If it gets really bad we turn it off or I can throw a blanket over his head.” (It didn’t come to that, she said.) Later that evening, her youngest son, 10-year-old Kyle, came downstairs to the living room and said he was already watching the show upstairs from his computer, recalled Ms. Leventhal. Since he was watching it anyway and she preferred he did so with her, she asked him to join them.

The show is a hot topic at 9-year-old Rocco Kotler’s school in Delran, N.J.

“It is very popular at school. Everyone wants to watch it,” he said. Those who do are “mostly the kids that have older brothers,” he added. Rocco said he recently got to sit with his father and two older brothers to watch two episodes on the family TV.

“He put his hand over his eye at one point,” said his father, David Kotler. Mr. Kotler said he paused before allowing Rocco to join, but decided that Rocco is mature enough, and that he would have stepped away if it had overwhelmed him. “You know your own kid,” he said.

Other parents are more worried.

Samantha Giddings, a teacher outside of London, said she would watch the first few episodes of the show before allowing her 13-year-old daughter, Emily, to watch it. Ms. Giddings said online forums have been filled with discussions about whether students should be watching the show. 

“I’m going to watch it and see what I think” before allowing Emily to tune in, Ms. Giddings said.

Emily hopes she gets the green light. “I’m really curious what the hype is,” she said.

Write to Anne Marie Chaker at anne-marie.chaker@wsj.com