The name comes from Leonard Richardson's robotfindskitten, a game described as a "Zen simulation." Robot moves through a field of unidentified objects, encountering them one at a time. Most are strange and whimsically described Non-Kitten Items, or NKIs. Eventually, robot finds kitten. There is no score to maximize, no opponent to defeat, and no way to lose.
The name also reflects a small connection between the press's author and the game's creator. Richardson later wrote What Fools These Mortals, a game for people who had played NetHack. In 2003, its website quoted the author's review, "I love this game!", under the author's name. For years, that brief endorsement was among the most prominent search results associated with the author online.
Non-Kitten-Item Press takes its name from this history and from the distinctive pleasure of encountering curious objects one at a time.