Is there any relationship between students' cognitive style and the ability to learn programming through serious games? The aim of this work is to assess the learning effectiveness and motivational appeal of digital games for learning basic programming concepts, involving secondary education students. For this purpose, the Code.org®'s activity named K-8 Intro to Computer Science was used. The study investigated students' attitudes from gaming activities to reveal the quality of their learning experience. Next, students' attitudes from games were correlated with their cognitive profile to reveal potential differences. Finally, students' performance from the digital games was assessed to reveal game-based learning (GBL) effectiveness compared to their cognitive styles. In the study, 77 students of two Greek high schools participated in the context of the European Code Week. The results suggest that these specific games, or similar educational computer games, can be exploited as effective and motivational learning environments within schools, as they provide a high-quality learning experience. Cognitive style was found to be a significant learning characteristic that should be taken into consideration when using digital games to learn programming.