Named because staying up all night hurts the liver. Specific meaning: spend a lot of time and energy playing the game to collect a certain equipment or character. Also known as bursting your liver. For example, stay up all night to play crazy hand game and then finally get a certain character (cards and so on) meaning, due to sleep late to hurt the liver. So here the "liver" noun is used as a verb stem, such as being known as the game liver to a certain character.

Then it was extended to doing something desperately, such as livering homework.