Investigators believe a gas leak in a heating system caused the fire in Koszalin, in the north of the country, and the girls - who were celebrating a birthday - were killed by carbon monoxide inhalation.
Koszalin prosecutor Ryszard Gasiorowski said it is believed that the fire broke out in the waiting room of the games room, "cutting off the employee who was supposed to supervise the participants of the game and help to unlock the door", leaving the girls trapped.
The room the teenagers were in did not have an emergency exit.
What are escape rooms and are they safe if players are locked in?
Escape room games, which have grown in popularity in recent years, see players seemingly shut inside a room or building with clues and puzzles to solve to help them get out or win a prize.
UK centres are monitored by staff throughout and players are made aware they can take an exit door in the case of emergency.
While questions have been raised about the safety of escape rooms following the fatal fire, "regulations in the UK are strict and standards are very high", David Middleton, the owner of , a Brighton-based escape room, explained.
The co-organiser of the escape rooms industry conference (ERIC) added that in the UK it is illegal for any business to lock a person inside a room, so players would never be trapped.
So escaping from an escape room is just part of the game?
"The name 'escape rooms' is misleading," Mr Middleton told ITV News.
"It probably comes from the escape the room video games," he continued.
"It's just an illusion of being locked in... players are welcome to leave at any time...
"Often the purpose of the game isn't even to escape from the room, it's to achieve a goal or find a gem, so you're not escaping at all."
What is done in the UK to make escape rooms safe?
"The UK escape rooms industry prides itself on high safety standards," Mr Middleton explained.
Like any UK business, escape rooms should ensure that "staff have proper training and that fire risk assessments are carried out," and that players are always supervised, he added.
An investigation has been launched in Poland following the deaths and the country's Interior Minster has ordered fire safety controls in all escape rooms.
Since Friday, more than 200 of Poland's 1,100 escape rooms have been checked, revealing a number of safety flaws that needed to be immediately fixed.
The 28-year-old who runs the escape room where the girls died has been arrested, his employee, who suffered burns in the fire, is also going to be questioned.
Sunday has been a day of mourning in Koszalin.