Even though the computerised assessment of developmental dysgraphia (DD) based on online handwriting processing has increasing popularity, most of the solutions are based on a setup, where a child writes on a paper fixed to a digitizing tablet that is connected to a computer. Although this approach enables the standard way of writing using an inking pen, it is difficult to be administered by children themselves. The main goal of this study is thus to explore, whether the quantitative analysis of online handwriting recorded via a display screen tablet could sufficiently support the assessment of DD as well. For the purpose of this study, we enrolled 144 children (attending the 3rd and 4th class of a primary school), whose handwriting proficiency was assessed by a special education counsellor, and who assessed themselves by the Handwriting Proficiency Screening Questionnaires for Children (HPSQ C). Using machine learning models based on a gradient-boosting algorithm, we were able to support the DD diagnosis with up to 83.6% accuracy. The HPSQ C total score was estimated with a minimum error equal to 10.34 %. Children with DD spent significantly higher time in-air, they had a higher number of pen elevations, a bigger height of on-surface strokes, a lower in-air tempo, and a higher variation in the angular velocity. Although this study shows a promising impact of DD assessment via display tablets, it also accents the fact that modelling of subjective scores is challenging and a complex and data-driven quantification of DD manifestations is needed.