I put this item on my HA for Masquerade, after purchasing it a few years ago from the Steamworks Menagerie:

However, after I put it on, I was still not allowed to dance with anyone, as the Wardrobe registered my HA as "not wearing a mask", even though this is literally an official Steamworks Menagerie mask-related item.

Is this intentional, or is it a bug?

It's not considered a mask because it doesn't have mask in the name. This is in the masquerade news post:

You can get around it by layering a small mask like under your avatar base.

As mentioned above, it's not a bug. :)