Arguably the grand goal of artificial intelligence research is to produce machines with general intelligence: the capacity to solve multiple problems, not just one. Artificial intelligence (AI) has investigated the general intelligence capacity of machines within the domain of games more than any other domain given the ideal properties of games for that purpose: controlled yet interesting and computationally hard problems. This line of research, however, has so far focused solely on one specific way of which intelligence can be applied to games: playing them. In this paper, we build on the general game-playing paradigm and expand it to cater for all core AI tasks within a game design process. That includes general player experience and behavior modeling, general non-player character behavior, general AI-assisted tools, general level generation and complete game generation. The new scope for general general game AI beyond game-playing broadens the applicability and capacity of AI algorithms and our understanding of intelligence as tested in a creative domain that interweaves problem solving, art, and engineering.