Unfortunately, there is no authentic or authoritative definition of "Delmonico Steak". The term was first used around 1837 to refer to the featured steak at the Delmonico Restaurant. Unfortunately, there is no written documentation of what cut of meat was used for that steak. Delmonico's is still in business and on their menu a Delmonico steak is a boneless ribeye, and many places serving a "Delmonico" also use boneless ribeye. But not everyone does, sometimes using any beef from the rib, short loin, or even the chuck eye.
A now long retired third generation butcher I bought from for years sold bone-in and boneless ribeye and a cut he called Delmonico. He claimed his father and grandfather taught him the technique and it was similar to what Delmonico's Restaurant used. His cut included only the main center muscle (ligmissimus dorsi) of the ribeye. He trimmed off the ribeye cap (spinalis dorsi), all connective material, and the larger pieces of external or intervening fat. This left a very tender steak that, because of the nice internal marbling, remained juicy and had great taste. I don't know if HAL or anyone else goes to this effort for their "Delmonico Steak", but the center piece of a ribeye is what I think of as a Delmonico.