The court however reduced the death sentence handed out to the alleged leader of IS in Kuwait, Fahad Farraj Muhareb, to 15 years in prison.
A lower court in September issued the death penalty to Muhareb and Abdulrahman Sabah Saud, who drove the suicide bomber to the mosque site on June 26.
It also handed out jail terms of between two and 15 years to eight others, including five women, and acquitted 14 others.
In Sunday's ruling, the appeals court acquitted one of the five women.
There was tight security for the hearing, with armored vehicles outside the Kuwait City court complex and helicopters patrolling overhead.
Judge Hani al-Hamdan said that the cases of five men sentenced to death in absentia for their role in the bombing were not reviewed because they remained at large.
Under Kuwaiti law, sentences issued in absentia are not reviewed by higher courts until convicts appear.
Four of the men at large are Saudis, including two brothers who smuggled the explosives belt used in the attack into Kuwait from neighboring Saudi Arabia. The fifth is a stateless Arab.
A total of 29 defendants, seven of them women, had been on trial on charges of helping the Saudi suicide bomber carry out the attack on a Shiite mosque in the capital, which was the bloodiest in Kuwait's history.
During the initial trial, Saud confessed to most charges but he denied all of them in the appeals court.
Among those acquitted Sunday was Jarrah Nimer, owner of the car used to drop off the bomber.
An IS-affiliated group calling itself Najd Province claimed the Kuwait City bombing as well as suicide attacks at two Shiite mosques in Saudi Arabia in May.
Najd is the central region of Saudi Arabia.
The Sunni extremists of IS consider Shiites to be heretics and have repeatedly attacked Shiite targets in the region.
Kuwaiti courts have already issued several verdicts on IS supporters and financiers.