Utsuge stands for utsu game, and it means "depressing game". It is said that the purpose of these types of games is to depress the player.

Most of the time these games have no happy end, no help, no hope...

Do not mix with a similar game type, nakige.

For example on an imaginary utsuge, the heroine would be sick from the very beginning and would die in the end. But on an imaginary nakige, the game would be about a happy school romance with the heroine suddenly getting sick at the very end of the game to only recover at the very last moment. (Though there are nakige with deaths too.)