When an -ing verb is applied to describe a noun, is it always an adjective? (or something else)

When an -ing verb is applied to describe a noun, is it always an adjective? (or something else)

For example: "A dancing ninja showed up today." - is "dancing" an adjective in this context? (In this case, referring literally to a ninja who dances.)

Specifically, in use: https://twitter.com/DrawmaticAR/status/1225527363489976320

It depends on the context. It could mean two things. The most likely is:-

... a Ninja (which is) dancing

In that case, dancing is a participle and so an adjective, qualifying the noun Ninja.

But, however improbably, it could also mean

a Ninja for dancing

That is, our Ninja might be a strange sort of dancing instructor. Unlikely, of course but grammatically possible. And in that case dancing would function as a noun (a so-called gerund), by analogy with ‘cricket bat’, where ‘cricket’ is strictly a noun, but is serving a bit like an adjective.

Nevertheless, despite this grammatical hall of mirrors, ‘dancing’ in your phrase is in all probability an adjective. Had you supplied a fuller context, we could be certain.