If a 1909-1916 Lincoln is a proof, then it is a matte proof, correct? There are no "non-matte proofs" for those years?

They made Matte Proofs in 1909-1916. They made Satin and Brilliant proofs in 1936. They made Brilliant proofs from 1936 - 1942. They started making brilliant proofs again in 1950, and continuously since. Check your Red Book for details.