I found many studies discovering the impact of game-based learning on motivation for learning.
You can also find a summary of them in this book chapter.
However, it is still unclear to me if this motivation is for entertainment or for learning. I was wondering if there is any study showing that students who are adapted to this method of learning have a higher motivation to pursue learning in other forms. My concern is about long-term effects of this method of learning. What is the intrinsic reaction of K-12 students who have adapted to game-based learning when they start higher education in which game-based learning is not provided? Will they have a higher incentive to study? or a lower incentive, because they prefer to play games rather than studying?
I'm a higher ed instructional designer. Our industry is beginning to integrate serious games(a term that seems to be replacing educational games) and the principles of gamification into our courses, particularly those that are online. We know that K-12 students are using Learning Management Systems, mobile devices, and games to learn (whether formally or informally), so we are getting ready for them.
On gaming versus studying: A well-designed serious game and/or gameified learning environment IS studying. Instructional designers like myself who are present on a team developing a gamified online unit of instruction or course are there to ensure that pedagogical best practices are embedded in the content. I can't really answer a generalized statement about higher or lower incentives/motivation because no specific audience has been defined. Individuals, and their reaction to different types of curriculum, vary.