Well as it turns out the triangular shaped font is also present on the round Gruen watch posted by
@Pierre1333.
However I’m not sure whether it should necessarily be called « Egyptian » because the beautiful silver watch with an Egyptian looking head posted by
@bubba48 has another type of font.
Also while the Gruen watch has what appear to be some scarab motifs on the dial, the enamel freezes around the case don’t look Egyptian at all.
Which is why I think those are all a bit of a mish-mash of styles, with the OP watch being predominantly art nouveau, @bubba48’s watch being predominantly art deco (despite the earlier style font), and the Gruen watch being sort of in between various styles.
In any event it would be interesting to find further documentation to determine how that font might be characterized.
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