The way I understand it (without seeing the actual study), it can be best explained thus:
We established that neoantigens are made by cancer cells. They basically give us a marker that lets us tell the immune system "look for this and kill it."
But there are multiple ways to do that. You could do it like a straight-ish sort of vaccine, where you just inject the peptides matching the neoantigen into the body. This is sort of how traditional vaccines work. You just say to the immune system "look at this, and teach yourself to fight it," and that does the trick with infectious diseases like measles, mumps, rubella, etc.
But it may be the case that the neoantigens in cancer, on their own, aren't really "different" enough for the immune system to pick them up and start killing cancer cells. Kind of like the immune system saying "Yeah this looks weird, but for tolerance's sake we'll let this one go."
What this study appears to be saying is that when you attach those neoantigens to the listeria protein in question, the body raises a more robust alarm.
Or rather, that was the hypothesis, and this study appears to support that hypothesis.
LONG STORY SHORT. Lots of pharma companies are trying to capitalize on neoantigens right now. This study suggests that the simplest approach, showing the body the neoantigens, isn't going to work so well. And when it doesn't work, ADXS's way appears to work.