If the game was just about words and phrases, no question her answer should be sufficient. But that game is also about the letters in the words, so I can see the case that she didn't enunciate every letter. No matter how they say it in everyday life, most people know that there's a difference between "-ing" and "-in." There have probably been phrases used on the show that intentionally use the "dropped g" ending, and the player would be expected to pronounce it that way. It does seem like it would open things to hair-splitting, though, since people enunciate letter combinations differently.
Whether the rules should be enforced so rigidly that they don't allow for the contestant's excitement and personal speaking style is another question; I'd be inclined to let her slide.