Definitely voltage sag.
I imagine if Jim were to use a LiFePO4 cell the runtime would be shorter, but output would be a lot flatter.
Edit:
He did use a LiFePO4. I posted without looking at the link, just remembering the E1D output curve from memory.
In actual use, it's just as described: turning it off gets me to full power again when the battery recovers, while leaving a long tail of decreasing outout till battery exhaustion.
I like this better than full output for X amount of time then rapid decline to nothing, so I use primaries exclusively in my E1D.