Specifically if you make a crossword type minigame, and the grid is on a solid color background, it does not count against anything . If you also create a detailed background for your crossword however that is different to the in-game background, that would be against the idea of a single background. The actual visual of the grid does not count against any other limits such as sprites or objects.
However an additional thing to look out for is that the minigame doesn't overwhelm the VN aspect - otherwise it won't be primarily a visual novel and thus would not qualify - this is a VN jam. With a 1000 word limit the time spent on the minigame may be disproportionally large, so only very short minigames are suitable.