I feel like this writer is using a rather idiosyncratic definition for empathy vs sympathy vs pity like saying empathy is where you actively worked to feel compassion but sympathy is where you feel it naturally because of similar circumstances for yourself? (Which is usually closer to the hallmark of empathy...)
"Temporal bandwidth" is the width of your present, your now... The more you dwell on the past and in the future, the thicker your bandwidth, the more solid your persona. But the narrower your sense of Now, the more tenuous you are. It may get to where you're having trouble remembering what you were doing five minutes ago.