I operated a similar case laparoscopically. this is an appropriate approach for omental torsion. I think laparoscopic surgery must be first option for all cases with acute abdomen.
This approach is best option especially in cases with non specific symptoms of acute abdominal disease, because preoperatively clinically is impossible to make exact diagnosis of omental torsion or infarction.
There is no doubt that laparoscopy should be the procedure of choice in this situation. Very well done! Peritonitis (localised or generalised) should no longer be considered a contradiction to laparoscopy in our times. One always has the option to convert if laparoscopy is unsuccessful.
Laparoscopy is a good diagnostic tool in case of "surgical" acute Abdomen anyway. There are pathologies that require open surgery however in this case laparoscopy was the choice for diagnosis and therapy.
It appears the tip of the appendix was adherent to the omental infarction. The unequivocal bloody peritoneal fluid & gross appearance of the omentum support a vascular etiology. I'm curious about the pathology found at the tip of the appendix.