It all depends on how you’re defining “influence”. As an example, let’s look at the first Resident Evil game and it’s predecessor, Sweet Home. More people have played or heard of Resident Evil than a movie tie-in game that was never officially released outside Japan. However, a huge amount of RE’s DNA (indeed, things that fans will say are necessary to capturing the feel of early RE games) stem from Sweet Home. Hell, RE was initially conceived of as a remake of Sweet Home, until they realized they didn’t have the rights. Below is an incomplete list of features from Sweet Home that were incorporated into the first RE.

• inventory management puzzles
• exploring an intricate, cohesive location inhabited by monsters.
• narrative communicated through found notes and cutscenes
• deliberately clunky combat to emphasize player vulnerability
• protagonist characters each have a thing they can do that others can’t (presaging Jill’s lockpick and Chris’s lighter)
• door loading transitions

So, which is the more influential game? The one that popularized all of these concepts, or the one that originated the concepts? I think a case can be made for both, but I lean towards the originator.