In modern usage, the act of removing a person's organs or entrails; in older usage, cutting something into pieces; or the present participle of 'gib' (to castrate).
From 'gib' (a castrated cat, or to remove organs/entrails), adding the '-ing' suffix. The term has both archaic uses (castration) and modern slang uses (video game violence).
In video games, 'gibbing' means bodies exploding into piece—the term is gaming slang that accidentally revived an archaic word from medieval animal husbandry, showing how gaming communities create their own linguistic time capsules!
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