Not being a gamer at all, I have very little knowledge of any of the DC-related RPG games/modules that came out over the last couple of decades.
Luckily Fantom Stranger Jacob T. Levy clued me in two Phantom Stranger appearances in in RPG modules--the first is this appropriately-titled one.
Sadly, I don't have any inside images available, but here's the description: "From the depths of a mystical dimension arises an ageless force of evil bent on earthly domination.
Under the guidance of the Phantom Stranger, the Justice League International must learn the secrets of an ancient tome in order to forever seal the Vengeance Gate, a dimensional portal separating the realms of chaos and order.
The race against deadly, arcane opponents is on--a journey to the corners of the globe--a harrowing adventure for the mightiest of heroes which begins when a stranger calls."