You may remember an X-Men film from last year with the same name as this game, and they do tell the same basic story. The difference, however, is the game is true to the 1981 comic book story line and the movie is... well, not. X-Men: Days of Future Past is also a regular paid game with no in-app purchases.
X-Men: The Arcade Game is a throwback to the days before X-Men: The Animated Series. That show, known for it's amazing title track and some pretty laughable moments, gave us the "traditional" X-Men lineup most of us know today. However, before that aired, there was a one-off pilot called X-Men: Pryde of the X-Men. In it, Wolverine had an Australian accent.
It was pretty horrible.
Pryde of the X-Men served as X-Men: The Arcade Game's inspiration; inside, you play as the X-Men that were present in the cartoon, and face the villains they faced, as well.