Background: The early diagnosis of autism spectrum disorder (ASD) is highly desirable but remains a challenging task, which requires a set of cognitive tests and hours of clinical examinations. In addition, variations of such symptoms exist, which can make the identification of ASD even more difficult. Although diagnosis tests are largely developed by experts, they are still subject to human bias. In this respect, computer-assisted technologies can play a key role in supporting the screening process. Objective: This paper follows on the path of using eye tracking as an integrated part of screening assessment in ASD based on the characteristic elements of the eye gaze. This study adds to the mounting efforts in using eye tracking technology to support the process of ASD screening Methods: The proposed approach basically aims to integrate eye tracking with visualization and machine learning. A group of 59 school-aged participants took part in the study. The participants were invited to watch a set of age-appropriate photographs and videos related to social cognition. Initially, eye-tracking scanpaths were transformed into a visual representation as a set of images. Subsequently, a convolutional neural network was trained to perform the image classification task. Results: The experimental results demonstrated that the visual representation could simplify the diagnostic task and also attained high accuracy. Specifically, the convolutional neural network model could achieve a promising classification accuracy. This largely suggests that visualizations could successfully encode the information of gaze motion and its underlying dynamics. Further, we explored possible correlations between the autism severity and the dynamics of eye movement based on the maximal information coefficient. The findings primarily show that the combination of eye tracking, visualization, and machine learning have strong potential in developing an objective tool to assist in the screening of ASD. Conclusions: Broadly speaking, the approach we propose could be transferable to screening for other disorders, particularly neurodevelopmental disorders.