Actually, that quote was the one sentence I didn't understand. Who's spilling the wine? And why does that buy tranquility? If you could help me that would be great :)
Most people are annoying: educate them or just put up with them, there is no third option. Also, always remember you are equally annoying to at least some of them.
I think the premise leading to the sentence is absurd: "And, if I pretended not to notice these slights, wasn’t I proving that I really was a disengaged, privileged oppressor?".
But the author is trying to reason with her anger in the face of perceived slights - verbalise it or hold it inside?
Epictetus suggests that small losses (of wine or of 'face') should simply be forgotten. They are sunk-costs whose expense has been incurred.
One need not pay more - in the form of one's tranquility or contentment - by dwelling on them.
The one argument against is of course justice, that is, punishing cheaters in prisoner dilemmas, special and general prevention, etc.
However, the Stoic would advise to do the punishment (where appropriate and possible) without anger, but rather as one would punish a child that has transgressed - for the benefits arising from it.
Which maybe works for yourself, but most of my significant others of the past would just start complaining that I lost a 20$ bill.