Well another matrix would give you random results. By using the same as the embedding matrix, the result when applied to a hidden state h will be a vector of size vocab_size where the coordinates  i will be the highest when h is similar to e_{i} the i-th vector of the embedding matrix. Why? If you do the math, the result of the decoder will have for coordinates the dot products h . e_{i} and, as long as every vector is bounded, is the highest when the cosine between h and e_{i} is close to 1.