I remember my younger, dreamier self thinking of life in this way. I think it's the people who are particularly attached to stories who tend to view their lives in this way. Stories—in particular, novels—have an important place in my life, and have at times affected the choices I made and how I want to live my life. Life doesn't present itself as a narrative, but it can if we edit and shape it into one. But I sort of like that life doesn't read like a single narrative. Life is much more interesting and varied in its raw format. I do like @chana's idea of "a series of short stories with a lot of filler in between". That feels more accurate.
The idea that the stories we're exposed to influences how we interpret our own lives (viewing them as narratives, for example) reminds me of that great piece that @Jonnyboy posted here, and in particular this passage:
Literature has taught her that moments of tenderness come in sporadic but knowable intervals. A girl who reads knows that life is not planar; she knows, and rightly demands, that the ebb comes along with the flow of disappointment. A girl who has read up on her syntax senses the irregular pauses—the hesitation of breath—endemic to a lie. A girl who reads perceives the difference between a parenthetical moment of anger and the entrenched habits of someone whose bitter cynicism will run on, run on well past any point of reason, or purpose, run on far after she has packed a suitcase and said a reluctant goodbye and she has decided that I am an ellipsis and not a period and run on and run on. Syntax that knows the rhythm and cadence of a life well lived.