This study represents the first stage of evaluating whether cognitive training interventions may be facilitated by the presence of a socially assistive robot (SAR) and gamification. Our experimental setup involves using a SAR providing feedback to a gamified visuospatial working memory task, administered according to a differential outcomes training (DOT) protocol. The study’s main objective was to investigate whether performance and attitude towards the task would be affected by different robotic setups (none, simulated or physical) and in relation to different challenge levels. We measured performance accuracy on the gamified visuospatial memory task and self-reported affective ratings, which are relevant for assessing attitude towards the task and providing indicators to the potential for using a SAR for a longer-term cognitive intervention. Additionally, we conducted exploratory analyses of eye movement strategies for memory encoding during the task. The results demonstrated a significant differential outcomes effect (DOE) on memory performance accuracy, regardless of Robot type and Challenge level, providing evidence that a DOE can still be obtained when a SAR interacts with participants. Moreover, the results from the affective ratings revealed that participants accompanied by the physical robot reported lower levels of stress and increased levels of control. Our results demonstrate, for the first time, a DOE using a SAR in a gamified context. This result, coupled with positive subjective reporting of the human–robot interactive experience of participants, demonstrates the potential for using a SAR to: (i) promote positive attitudes for a DOT-based cognitive intervention, without (ii) negatively affecting task performance.