this one time introduces a story taken from the speaker's set of personal experiences.
this is the verbal equivalent of the speaker using his index finger to point at something. And just like an index finger pointing at an object, the word this is used from the speaker's vantage point or perspective. People frequently expect you to know what they're pointing at, even if from your angle it is not always clear what they're pointing at. The same is true with speakers when they use the word this. It won't always be immediately clear what they are referring to. Sometimes listeners must imaginatively adjust their perspective to be in line with the speaker's perspective, in line with the perspective of the person who is pointing at something.
There is a linguistic term for this basic phenomenon of perspective in verbal communication: deixis.
One of the main differences between fingers and words is that fingers can point only at actual objects, whereas words can point to ideas and thoughts and memories. The speaker in your example has in mind a collection of memories, stories he could tell about "cool" Adolf. When he says "this one time", he is pointing a virtual finger at a particular occasion from his collection of memories.
Native speakers understand the collocation this one time to be an introduction to a personal story.