The edited question seems to be more clear, so let me suggest another translation:
The literal one-to-one translation does not work every time, especially if it is about a pair of distant languages.
In English phrase, "gaming series", the "gaming" is an Adjective, but its role is much more than describing a noun "series". Compare:
- what kind of series? — gaming series. Here, gaming denotes some kind of a attribute of series; Just replace "gaming series" to "interesting series" or "boring series" to see the contrast.
- series of what? — series of games. Here, games is the key word in the pair. In other words, not just games, but a sequence, series of it.
You can also consider an inversion: serial games, which seems to be a more specific expression (albeit less used).
In Ukrainian, Adjectives are used primarily to denote the property of a Noun (1st case listed above). So instead of trying to fit an Adjective here, I would prefer a pair of Nouns: серія ігор, literally, series [of] games
Examples are countless. Here's my favorite:
Civilization (укр. Цивілізація) — серія відеоігор жанру глобальних покрокових стратегій […] — Wikipedia
Відеоігор here is a compound Noun відеогра (відео+гра)
+PLR+GEN (Plural number, Genitive case)