It's like an extended Twilight Zone episode. The tone's both more deadpan and less earnest, but I could absolutely imagine that show telling this story. Especially the finale. You could probably even edit it down into a half-hour TV episode, since it's so minimal and straightforward.
A cafe owner (Kato) finds that his TV monitor is showing images from two minutes into the future. He has a Steven Moffat conversation with himself, although both versions of him are confused. The waitress at his cafe finds out about this and calls over two friends. Soon they're all playing around with it, doing experiments, completely failing to worry about bootstrap paradoxes, etc. (There's a line towards the end about causality breaking down.) There's a mini-blackboard on which people draw diagrams. It's quite fun.
This is a low-budget film that doesn't have the resources to do anything big with its idea. That's fine. It works as it is. It was actually shot by members of a theatre troupe. The film's big gimmick is that it's another one-shot Japanese film, a micro-genre that appeared after the success of One Cut of the Dead. (They even have a word for it: "nagamawashi".) This is surprisingly fascinating, because I was wondering how the hell they got all those TV conversations to line up. It was shot in real time, after all. Where did the time-lapsed footage come from? Did they shoot it beforehand? Did they composite it in later? Did they shoot multiple takes of this film and stream previous takes in as the TV footage? Or did they actually fake the whole "one-shot" thing, editing together multiple takes with surreptitious CGI to hide the joins? I've no idea, but it's seamless.
Also, the film was shot on a Tamagotchi-sized camera, strapped to the back of a smartphone.
I don't mind the bootstrapping. The story feels very Steven Moffat to me, after all. No, the bit I didn't buy was the explanation of "Droste effect" in which Kato happens to have one of the original 1904 Droste cocoa tins in his little Japanese cafe. Uh-huh.
The film's fun and I enjoyed how carefully it's thinking through its idea... but its first half is just friends getting excited and playing with a time TV. The film eventually grows a plot, but not until there's only half an hour left. It's an understated, unspectacular film, but it's amusing and sometimes even funny. Kato's conversation about Nostradamus and the Mayan calendar made me laugh. This one's worth a look.