Thanks! Coincidentally, I also found Dylan’s article (as well as another study from 2015) and added an answer based on it, before seeing yours.
EDIT: Oh, I now see that you were linking to an earlier piece by Dylan from mid-2015, also published in Vox. The article in my answer is from late 2018.
This Vox article by Dylan Matthews cites these two studies, which try to get at this question:
Bendavid & Bhattacharya (2008) — finds 1.2m deaths averted in twelve countries from ~2004–7
Bendavid et al. (2012) “found that PEPFAR reduced all-cause adult mortality in affected African countries by 16 to 20 percent.”
EDIT to add: here’s a more recent analysis, looking at mortality impact up to 2018 — Kates et al. (2021)
Thanks! Coincidentally, I also found Dylan’s article (as well as another study from 2015) and added an answer based on it, before seeing yours.
EDIT: Oh, I now see that you were linking to an earlier piece by Dylan from mid-2015, also published in Vox. The article in my answer is from late 2018.