I had been calling it pre-echo myself without realizing it's a real thing. I must have a dozen recordings where this occurs and always wondered if it had to do with the quality of mastering equipment in 80s or perhaps not being familiar with side effects of trying to be clever. One thing is for sure though: Quality control was severely lacking at even the largest of companies and productions.Coincidentally, in reference to the Reddit post, I almost typed, "pre-echo", as a third possible name.
I've studied audio engineering, and therefore familiar with most editing techniques.
Unfortunately (or fortunately, as the case may be), the pre-echo sound seems to be edited-out of my digital copy of the Gabriel song.
drftr