It was a few years ago that I last experienced KWI, but, yes, your itinerary would require a visa. They had visa-on-arrival, where you stand in a line airside and pay a fee then proceed to immigration. This is one of the least appealing capital airports in the world (unlike the new MCT, which is excellent). Not sure if you'd be able to check your bags that early or if there is a left-luggage counter, but with that time frame you might as well take a taxi and explore Kuwait, though there isn't much to see.