Advertiser’s Gothic.
Early 20th Century, American.

Art Nouveau, without question. From Wikipedia…

The first use of the term Art Deco has been attributed to architect Le Corbusier who penned a series of articles in his journal L'Esprit nouveau under the headline 1925 Expo: Arts Déco. He was referring to the 1925 Exposition Internationale des Arts Décoratifs et Industriels Modernes (International Exposition of Modern Decorative and Industrial Arts).

No doubt the idea of curving the straight bits came from Art Nouveau, but it evolved into Art Deco, through the efforts of people like Wiebking.

Looking at the history of the Mennen brand, it adopted a version of this bendy style in the teens, and used it for the wordmark—and still do!—and in packaging and advertising typography in the teens and twenties.

Advertiser's Gothic is a tour de force by Wiebking, in which he managed to successfully integrate three design themes—curved straights, stencil, and vestigial descenders.

Another face from the same era, Poor Richard, has the similar stencil effect:

All those styles, or parts thereof, were lettered in ads, posters and packaging before being made into type, and again, who knows where they originated? They may even be considered design by a cadre of lettering artists bouncing themes around. “Poor Richard” was hand lettered on many a silent movie intertitle.

Also in the same vein: Arts & Crafts lettering, e.g. by Rennie Macintosh and Dard Hunter (1908):

It’s doesn’t do justice to Advertiser’s Gothic to pigeon-hole it as influenced by Art Nouveau. All one can do is point out similarities—who knows what went through Wiebking’s head? Not even him, no doubt, and the only way he could find out was to draw and cut the face, and then see what it looked like.

Perhaps it could be said that it was influenced by Art Deco from the future — an emergent principle.