I think you just confirmed the very point of the poster you criticized. By the way, you chose one of many uses of Sarcasm to suit your purpose of attacking the poster. His/Her use of the word "Sarcasm" still applies. Sadly, the list below reads like a description of one of your frequent posts on this site.
Synonyms of Sarcasm:
affront, barb, brickbat, cut, dart, dig, dis (also diss) [slang], epithet, gird, indignity, name, offense (or offence), outrage, personality, poke, put-down, insult, slap, slight, slur, catcall, gibe (or jibe), jeer, mock, quip, sneer, taunt; abuse, invective, vituperation; disapproval, opprobrium; disgrace, dishonor, shame; attack, criticism, knock, slam, swipe; torment