Drivers of conditionally automated vehicles may occasionally be required to take control of their vehicle due to system boundaries, but their performance in such cases might be impaired if they were engaged in non-driving tasks. In this study, we conducted an experiment in a driving simulator, where the non-driving task involved playing a video game. We tested whether, after a take-over request (TOR), driver behaviour can be predicted from measures of game engagement. A sample of 28 participants drove in two counterbalanced conditions—manual driving and automated driving—and needed to change lanes at a certain time in their trip following auditory and visual requests. In the automated condition, drivers could play an endless runner game and were instructed to deactivate the automated mode to change lanes when they received a TOR. We used the proportion of glance durations on the game and the time between game sessions as indicators of game engagement. Findings showed that drivers were highly engaged in the video game during the automated driving session (more than 70% of the time) and that the inspection of driving-related areas of interests was significantly altered by this engagement. Moreover, the two indicators of game engagement predicted drivers’ response times to the TOR. Our findings suggest that indices of game engagement might assist in setting better timing for TORs and therefore, that it might be beneficial to synchronize measures of game engagement consoles with automated vehicle decision algorithms.