Computational thinking (CT) is a broadly used term in education to refer to the cognitive processes underlying the application of computer science concepts and strategies of problem-solving. Recent literature has pointed out the value of children acquiring computational thinking skills (i.e., understanding and applying concepts, such as conditionals, iteration, or generalization), especially while learning STEM subjects. Robotics has been used as a tool to introduce computational thinking and STEM knowledge to children. As physical objects, robots have been proposed as developmentally appropriate for the early childhood setting, promoting motivation and allowing young learners to represent abstract ideas in a concrete setting. This study presents a novel educational robotics (ER) intervention using RoboTito, a robot programmable through tangible elements in its environment designed for kindergarteners. We used a quasi-experimental design with an active control group. In addition, we conducted a structured observation of the filmed material of the sessions to gather data on children’s attention and motivation throughout the activities. Fifty-one children (male = 33; mean age = 66 months, SD = 5.49 months) attending level 5 (kindergarten) at a Uruguayan public school participated in the study. Children in our experimental condition participated in an intervention programming RoboTito using tangible elements, while children in our control condition played with the robot through sensory-motor activities using a remote control and did not engage in programming. Motivational and attentional factors were assessed through video-recorded sessions of the ER activities. Four trained observers blind to the experimental conditions participated in the coding. Children’s interactions were assessed in four categories: task engagement, distractibility, oral participation, and objective fulfillment. Our results suggest children’s task engagement mediated their gains in CT after the intervention; post-hoc Tukey contrasts revealed non-significant pre-test to post-test gains for the control and low engagement groups, and significant for the high engagement group. Overall, we conclude task engagement played a central role in children’s learning gains and our robotics intervention was successful in promoting CT for engaged children. We discuss the practical implications of our results for early childhood education and developmentally appropriate ER targeted for young learners.