Should a weight gaining diet be focused on calories or protein?

It should focus on both. While calories alone will cause you to gain weight, pretty much regardless of protein content, a modest amount of protein can help promote an increase in lean muscle mass, especially when combined for resistance exercise. Roughly 1.5 grams of protein per kg of body weight per day (~.7 grams of protein per pound of body weight for the metrically challenged) is about the highest that's been shown in studies to be effective.