They are present participles part of a compound adjective. The fact that the adjective is compound as you say, it doesn't make it less of an adjective:
running water means water that runs
flourishing business means business that flourishes
English-speaking countries means countries that speak English.
A present participle is a word that (1) ends "-ing," (2) is formed
from a verb, and (3) is used as an adjective or to form verb tense.
In combination with a noun or adjective, present participles form compound adjectives:
A compound adjective is an adjective that contains two or more words.
In general we put a hyphen between two or more words (before a noun)
when we want them to act as a single idea (adjective) that describes something.
- I live in an English-speaking country.
English-speaking is an adjective (used to describe the country). We
use a hyphen to connect the word English with speaking to show that it
is one adjective (or one idea).
So all these are verbal adjectives, and Wikipedia draws attention to a distinction between verbal and deverbal adjectives:
In English (and in most European languages), verb forms that can be used attributively are typically non-finite forms — participles and infinitives — as well as certain verb-derived words that function as ordinary adjectives. All words of these types may be called verbal adjectives, although those of the latter type (those that behave grammatically like ordinary adjectives, with no verb-like features) may be distinguished as deverbal adjectives.
An example of a verbal adjective with verb-like features is the word wearing in the sentence
- The man wearing a hat is my father (it behaves as a verb in taking an object, a hat, although the resulting phrase wearing a hat functions like an attributive adjective in modifying man).
An example of a deverbal adjective is the word interesting in
- That was a very interesting speech; although it is derived from the verb to interest, it behaves here entirely like an ordinary adjective such as nice or long.