A eureka moment struck, recalls Mr. Rippel. “Hey, hold on, we could do this for real.”

WaveOne Inc., the startup founded by Messrs. Bourdev and Rippel, is using an artificial intelligence technique to improve upon existing real-life compression technology. And they are finding early success, according to a paper they submitted to an academic conference on Thursday. WaveOne hopes its progress will help it recruit engineers and excite potential customers.

Just like their fictional analog, which faces stiff competition from tech giant “Hooli,” the WaveOne team fears its toughest test could be competing against what some argue is Hooli’s real-life corollary: Alphabet Inc.’s Google.

The search giant has a team of researchers working on similar video compression technology, a Google spokesman confirmed. Other companies are also working on the technology.

An HBO spokeswoman didn’t respond to a request for comment.

The six-person team at WaveOne says it isn’t very much like Pied Piper’s band of brilliant weirdos, which includes a self-described Satan-worshipping software engineer; his sparring partner, a Pakistani-born nerd with dry wit; a curly-haired pot smoker totally lacking in self-awareness; a skinny, self-sacrificing organizer who will go to extreme lengths to please the boss; and their naive, anxiety-crippled leader.

“We’re a linear combination of their personalities,” says Alexander Anderson, a research scientist at the company.

They’re also more athletic. Mr. Anderson, 28, loves Bollywood and hip-hop dancing. Steve Branson, 37 and another research scientist, is an expert rock climber. Mr. Rippel, 30, once taught the Israeli martial art Krav Maga after his postcollege service in the Israel Defense Forces. He declines to discuss details: “A lot of that is classified.”

The company’s single conference space in its small, whiteboard-walled offices is called “The Interrogation Room.” There they interview potential recruits, “people who we suspect will infiltrate our org,” jokes Mr. Bourdev, 43.

While keeping the company’s work secret from rivals is a priority, he says, Mr. Bourdev’s attempts to do so could probably inspire their own “Silicon Valley” episode.

They once had a rival researcher over to the office for a social call, they say. Everywhere it said “video compression” on an office whiteboard, someone jokingly scribbled the word “Not” in front of it, hoping the engineer wouldn’t notice.

At a conference Mr. Bourdev attended, he hatched a plan to tell anyone who asked whether his company was working on video compression, “We could tell you but then we’d have to hire you.” The only person who asked was a senior Google researcher too advanced in his career for the startup to offer a job.

Video compression is used to encode video files so they take up less storage space and are easier to transmit over the internet, mostly by eliminating redundant information. The hope with artificial intelligence is that it can eliminate more data by making accurate predictions about video frames that are coming next, meaning consumers could get the same picture quality from fewer bits sent through the pipe.

After reviewing WaveOne’s paper, Alan Bovik, director of the laboratory for image and video engineering at the University of Texas, said its early results “seem pretty fantastic,” but cautioned the company needs to show its techniques work with more kinds of data.

The WaveOne team has had fun with its fictional counterpart. Its first academic paper on more basic image compression, published at a 2017 conference, included a nod to the show and its creator: “Pied Piper has recently claimed to employ [machine learning] techniques in its Middle-Out algorithm (Judge et al., 2016), although their nature is shrouded in mystery.”

The reference was spotted by a commenter on the website Hacker News, who accused WaveOne of being a marketing stunt by the show’s creators to drum up interest.

Google, meantime, has acknowledged comparisons to the show’s tech giant Hooli. The company hid a link to Hooli’s satirical website in the 2015 blog announcing its reorganization.

Sometimes “Silicon Valley” gets even closer to reality.

Ilir Sela, owner of online pizza-ordering service SliceLife, was floored in March when the Season Five premiere featured a fictitious pizza company named SliceLine stealing engineers from Pied Piper.

Mr. Sela knew to watch the show since his product manager Finn Borge told co-workers to tune in. Mr. Borge swears he had no idea what was coming, that a friend of his girlfriend knew the writers, was aware of the similarities, and got word to him to alert his team. After the episode aired, someone from the show delivered a SliceLine pizza to the SliceLife office.

A person familiar with the SliceLine episode says the name similarity was purely a coincidence.

One of the show’s creators, Mike Judge, is no stranger to inspiring real-life business plans. His movie “Office Space” made red Swingline staplers so famous the company had to start making red ones to meet demand. Mr. Judge didn’t respond to a request for comment.

Mr. Bourdev says he was once chatting with his old Facebook boss, Chief Executive Mark Zuckerberg, and reminded him that his startup was working on better compression. He says Mr. Zuckerberg cracked that if the WaveOne team could demonstrate a high Weissman score—a fictitious test of compression efficiency developed for the TV show—their technology might interest them. A Facebook spokeswoman declined to comment.

The pair’s a-ha moment nearly fizzled that day they were first watching the show together. Mr. Rippel, googling to see if other startups were onto the idea, found a website for one that seemed to have a head start. “I had this ‘oh shit’ moment,” he recalls, “there’s a company doing that.”

Turned out he’d not been watching the show closely and was fooled by the authentic-looking website its creators had posted for the fictional company, Pied Piper.

Write to Rolfe Winkler at rolfe.winkler@wsj.com