Mark was not an exact remake of LAM. Some story elements and characters were changed or added to.. and of course, playing up on the Browning/Lugosi success with Dracula a few years before. Browning did make this version more of horror/vampire-themed story.
In LAM, (from the reconstruction and script) there is a scene where Chaney is shown putting on his vampire makeup, to go under cover, so this is quite different than films which featured a blood sucking creature/monster (Nosferatu, Dracula) as a principle character.
In the end, the audience learns, too, that Lugosi and Borland were also 'actors' in Mark -- hired to help trap the real murderer.
This film, tho, was more promoted to be a horror movie-- and the Lugosi/Browning re-team was certain to help that element, too.