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But (spoiler alert) at the end Groundhog Day, he does eventually go forward. The loop breaks, so he does eventually, in the last iteration, merely go back a day and then keep moving forward. So even under this definition, one would have to say that Groundhog Day eventually does depict time travel -- during the last iteration of the day.
If a loop breaks the time line has to move forward and it would do so from the end of the last cycle. It so happened in the Groundhog Day that in the last cycle Bill Murray's character was able to fall in love with Andie Macdowell's character and the movie had a happy ending. If any other loop would have been broken, the story would theoretically have progressed from there. My point is simple, each of those loops did not have any impact on Andie Macdowell's character, did they? She was charmed by Bill Murray's character many times, but that did not have any bearing on the final cycle. He started afresh and was able to make her fall in love with him all over again.
Also, the idea of time travel necessarily changing events in the future is definitely not a universally-held hallmark of the concept, at least in fiction. Many stories (like Lost, for example) feature time-travel that is self-fulfilling. IE: someone goes back to stop something, only to learn that their attempt to stop the thing is what causes it in the first place. Under the definition you're offering, these wouldn't be time travel stories, either, because they exert no ability to change things. The thing that happened is destined to happen one way or another, and their knowledge of it is a part of that destiny in the first place.
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