The word 組子 compounds 組 (kumi, to assemble or set in order) and 子 (here a diminutive for small members). In tategu — the trade of architectural fittings — kumiko are the slender muntins that fill a frame. English usage has widened the word to mean the whole decorative lattice, and then the craft of making it.
Wikipedia’s short article, drawing on trade sources, describes thinly slit pieces that are grooved, punched, and mortised, then fitted with plane, saw, and chisel. Panels “slot together and remain in place through pressure alone.” That interlocking-strip method is kumiko. A graphic of the same pattern, cut from a sheet, is a different object. See Hand vs CNC vs laser.
Rice glue and paper are ordinary in shōji covering. The lattice members interlock; they are not nailed through like a Western grill.