Are movies where the time loops over and over considered time travel movies?

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?