I think it depends on the method for the loop, and how time itself plays into the plot.
Like, I wouldn’t say Groundhog’s Day is a time travel story. But Deathloop (the game) is a time travel story. The main reason for this is that Deathloop explicitly tells you that the loop is caused by a time machine device, where as Groundhog’s Day could be interpreted as Bill Murray having died and is now in Hell or Limbo.
The way you escape the loop in Deathloop is to get all the looping people to die and then destroy the machine. In Murray’s situation in Groundhog’s Day, the solution is to… Be a better person?
Edge of Tomorrow.
Plot - Earth is invaded by aliens. Tom Cruise gets a power where if he dies, the day starts over. So, he keeps pushing forward in the warzone, and if he dies, he knows how he’ll get attacked and adapts to it.
I’m confused, do you think this is a request for time loop movies?
The premise of time travel movies is a person being able to be present at a different time to their original timeline. So I guess you could say a Groundhog Day type of movie is a subgenre of the time travel genre.
Okay, maybe sub-genre is the proper phrase I was thinking of. Thanks!