Dark chestnut. I have a gelding who is a very similar colour; a nice rich red body with a very dark mane & tail. Even has similar smutt marks on the rump.
The term liver chestnut is generally applied to chestnuts who are darker all over. Although really, there is no known genetic difference between the different shades of chestnut. They all carry the ee genotype. He's definitely not a bay as he doesn't have the black points, and even the lightest shade 'wild bay' has minimal black points up to the pasterns. Bays carry the Agouti gene which can only be expressed on a black phenotype (Ee or EE) and is masked when present in the chestnut (ee) phenotype.
My chestnut boy for comparison