I see nothing in the definition that makes that distinction. It does not have to be immediate or personal.
People are just unnecessarily adding their own negative connotations to the word.
revenge
/rɪˈvɛn(d)ʒ/
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noun
1.
the action of hurting or
harming someone in return for an injury or wrong suffered at their hands.
"other spurned wives have taken public revenge on their husbands"
synonyms:vengeance, retribution, retaliation, reprisal, requital, recrimination, an eye for an eye (and a tooth for a tooth), tit for tat, measure for measure, getting even, redress, satisfaction, repayment, payback; More
verbLITERARY
1.
inflict hurt or harm on someone for an injury or wrong
done to oneself.
"I'll be revenged on the whole pack of you"
synonyms:take revenge on, exact/wreak revenge
revenge (usually uncountable, plural revenges)
Any form of
personal retaliatory action against an individual, institution, or group for some alleged or perceived harm or injustice.
https://en.m.wiktionary.org/wiki/revenge