I really enjoy puzzle games especially if they have a story to them, e.g. Journey Down, Monument Valley, The Room (and its sequel), Device 6, and Tengami. While this is more heavy on the gameplay rather than story, it builds a wonderful universe and is excellently challenging. I spent three days fanatically playing the levels despite having fifty pages or so of research papers (which I completed on time without worry). Would buy again, waiting for sequel, etc.
Adriennethology about Tetrobot and Co.