Domain generalisation involves learning artificial intelligence (AI) models that can maintain high performance across diverse domains within a specific task. In video games, for instance, such AI models can supposedly learn to detect player actions across different games. Despite recent advancements in AI, domain generalisation for modelling the users' experience remains largely unexplored. While video games present unique challenges and opportunities for the analysis of user experience -- due to their dynamic and rich contextual nature -- modelling such experiences is limited by generally small datasets. As a result, conventional modelling methods often struggle to bridge the domain gap between users and games due to their reliance on large labelled training data and assumptions of common distributions of user experience. In this paper, we tackle this challenge by introducing a framework that decomposes the general domain-agnostic modelling of user experience into several domain-specific and game-dependent tasks that can be solved via few-shot learning. We test our framework on a variation of the publicly available GameVibe corpus, designed specifically to test a model's ability to predict user engagement across different first-person shooter games. Our findings demonstrate the superior performance of few-shot learners over traditional modelling methods and thus showcase the potential of few-shot learning for robust experience modelling in video games and beyond.