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I say no.
Time travel stories are about going to a different time.
Time loop stories are repeating the same time.
It's really that simple.Time loops are anti-time travel really, as there's no movement in time at all.
What about stories about time travel that ultimately form a closed loop? There's one that has people moving forwards and backwards through time, yet forms a closed loop at the end: >!Dark!<
A closed loop story creates consistency.
Groundhog loops are different each loop
If they're using time travel to create a causality loop, that's different than a time loop.
Time loops usually reset causality, accept for those actually experiencing the loop iterations.
I'm not sure that it can be clearly delineated as a time loop or a causality loop, it's honestly a mix of both - though you'd probably call it a causality loop, as each "instance of a person" only experiences the loop once.
predestination is a mix then? it's a loop, but selected time periods.
what about time crimes?
Haven't seen it, but sounds like it. Time travel can certainly be used to create loops.