In this case they convey a subtext you can’t get as gracefully by being a slave to syntax— that the author hoped the post would be about how they did achieve success, but that didn’t happen, forcing the parenthetical qualifier. I don’t think another treatment would express that quite as well; you can almost feel the wince.
> I love this [...] use of parentheses. [Rules] can be just as powerful when violated as when upheld.
You've offered a linguistically prescriptive interpretation that ignores nuance and flexibility of language.
While it may be the case that the canonical "point" of parenthesis is what you've described, the purpose only remains for as long as we culturally accept that definition.
The usage of parenthesis as an aside to indicate a certain emotion somewhat playfully is not only acceptable, it's entered into the cultural zeitgeist. We all understand the meaning. The sentence is complete -- regardless of the rules you've cited -- because the reader doesn't eliminate the parenthesis from their context like a robot, and we have a common understanding of what the aside is trying to communicate.
The right way is to replace the parentheses with a pair of dashes, one before and one after the deemphasized clause
Or maybe:
"... trying (unsuccessfully) to succeed..."