gateway game 

A game (esp. role playing) that can lead to 'heavier' and more time-consuming games as addiction progresses.

At first Baldur's Gate was just a reprieve from the daily grind, but slowly I found myself lusting after more rpg's, even pen-and-paper type games. It was at then that I realized I was in the clutches of a gateway game.

gateway game by Necrotaur July 16, 2003

Gateway Game 

Much like a gateway drug, a gateway game is a game which introduced someone to playing video games.

Previously, gateway game consoles were strictly Nintendo. As time progressed, the console that the gateway games are played on have progressed as well.

Normally, a gamer with an older sibling is introduced to their gateway game by their older siblings. In this situation, the young gamer tends to play many gateway games.

Many consider Super Mario 64 to be the first gateway game for many gamers.

Jacob: Yo, Jackson! I just played the best game at Kyle's house! Call of Duty: Black Ops, I need to go and get a Xbox 360 so I can play that great game.
Jackson: Welcome to the world of gaming, although you could've picked a better gateway game.

Gateway Game by Japas January 22, 2014