When you are "long gamma", your position will become "longer" as the price of the underlying asset increases and "shorter" as the underlying price decreases.
My intuition tells me that if you're long gamma, all that means is that if gamma increases, so does the value of your portfolio. Correct me if I'm wrong, but this seems to conflict with the quoted definition above (it is possible for gamma to decrease while the value of your portfolio goes up). Am I totally wrong? Does being long gamma simply mean your portfolio has a positive gamma as the quoted definition suggests?