NC claims the 1932 Karloff film is the original (true) and superior (arguably true), but then dumps on the 1999 "Mummy" despite the clear parallels between the two. He complains that the 1999 Mummy doesn't appear until an hour in? In 1932, Imhotep wasn't even revealed to be Ardeth Bey until around the 40-minute mark, and that's a film that's only about 70 minutes long. The Ardeth Bey revelation was akin to the Mummy appearing, since aside from a brief, mood-setting scene in the very beginning, the 1932 film doesn't actually feature a classic walking Mummy at all.
The curse granting Imhotep power? Yes, that's because both films--and ALL of these films--derive from the same basic "curse of the pharaohs" narrative, as established in the latter half of the 19th century. By establishing the Mummy as a person and agent/sender of the evil forces acting against our protagonists, the storytellers needed a reason for him to carry those forces: hence the advent of the Mummy as a cursed, unnatural being, one whose existence perverts the world around it in the manner of a classic agent of chaos. In fact, the 1999 treatment makes a little more sense than the 1932 one, since in 1932 the origin of Imhotep's powers was vague and trailed perilously close to "just a creepy Oriental thing."
The comedic tone? Not so much in 1932, granted, but from 1940 onwards Universal and Hammer Horror were both known to put in a little comic relief in the form of hapless sidekicks, wise-cracking men at the pub, etcetera. (NC also complains about a lack of one-liners at key moments, so … make up your mind, Doug.)
The adventure aspect? Mummy films have always had something in common with adventure serials. Consider the protagonists in any given black-and-white Mummy film: sure, there's the gray-haired professor who actually knows things, but the lead character is always a strong-jawed man with sleeves rolled up and a pistol to hand. The roots of the story come from the waning days of the British Empire, when colonialism was A Thing and Kipling lauded the Sudanese with these words: “You're a pore benighted 'eathen, but a first-class fightin' man.” Adventure meant exploring exotic foreign places and uncovering their hidden secrets, and sometimes getting killed by them. Complaining about adventuring and fighting in a Mummy film is like complaining about the yeast in your beer.