Social experience can deeply impact on gaming experience and is often used to increase enjoyment and retention. In the literature two main categories of social interaction can be identified: competition and collaboration. Player engagement has been widely studied under different conditions related to the type of social interaction taking place during the game. However, rich and newly available contexts based on emerging paradigms, such as those enabled by Natural User Interfaces, have not been yet extensively addressed. In the current study the impact of collaborative and competitive goal structures on player engagement, awareness and social presence is evaluated in the context of a jigsaw puzzle game taking place in a Shared Virtual Environment using a highly immersive setup exploiting natural user interaction.