Before Gibs, There Were Bits
When designing Doom, one of the concepts would be to have spectacular deaths for enemies who took overwhelming damage. The term for this extreme state of disrepair was originally called " bits" as in "blown to bits," but this concept was eventually canonized as gibs by Adrian Carmack. True gibs as they are now understood, though, did not emerge until later. At the time, enemies in Doom simply had an alternate sprite animation for their destruction, which showed them being torn apart into a pile of bloody gore. This was still a single, dead sprite, though, and not a group of objects that separated from the target.
Gib as a verb refers to killing a character such that they are turned into gibs, which usually means that no intact residual corpse is left behind. This may be important if the existence of a corpse is necessary for some facet of gameplay, such as a resurrection ability requiring a target corpse for use or loot not being dropped by a character whose corpse is destroyed.