I think I know why venting reduces anger. It's not the venting itself. It's someone hearing you and validating your feelings on the matter
(also why it doesn't always work, especially if people shit all over you for it)
.......I'm skeptical of that top article because as written it's really unclear whether the study looked at immediate or long-term strategies.
acute and chronic conditions aren't the same things, so that's kind of a profoundly important distinction that doesn't... seem to be there anywhere
some of the wording kind of makes me think the study mainly looked at long-term strategies (i.e. the things you have a weekly schedule to do for general stress relief etc), but the article then talks about what sound like acute anger (e.g. mentioning "counting to ten")
I can definitely believe that habitual, programmatic venting can be unhelpful for many or even most people, since (as suggested in the article) it can be habit-forming and it's not targeted the same way as venting in the moment
...but the article seems to try to assert that exertion and expression doesn't reduce anger in the moment, either, which just seems inconsistent with observation