The collection and the analysis of kidney stone morphological criteria are essential for an aetiological diagnosis of stone disease. However, in-situ LASER-based fragmentation of urinary stones, which is now the most established chirurgical intervention, may destroy the morphology of the targeted stone. In the current study, we assess the performance and added value of processing complete digital endoscopic video sequences for the automatic recognition of stone morphological features during a standard-of-care intra-operative session. To this end, a computer-aided video classifier was developed to predict in-situ the morphology of stone using an intra-operative digital endoscopic video acquired in a clinical setting. The proposed technique was evaluated on pure (i.e. include one morphology) and mixed (i.e. include at least two morphologies) stones involving "Ia/Calcium Oxalate Monohydrate (COM)", "IIb/ Calcium Oxalate Dihydrate (COD)" and "IIIb/Uric Acid (UA)" morphologies. 71 digital endoscopic videos (50 exhibited only one morphological type and 21 displayed two) were analyzed using the proposed video classifier (56840 frames processed in total). Using the proposed approach, diagnostic performances (averaged over both pure and mixed stone types) were as follows: balanced accuracy=88%, sensitivity=80%, specificity=95%, precision=78% and F1-score=78%. The obtained results demonstrate that AI applied on digital endoscopic video sequences is a promising tool for collecting morphological information during the time-course of the stone fragmentation process without resorting to any human intervention for stone delineation or selection of good quality steady frames. To this end, irrelevant image information must be removed from the prediction process at both frame and pixel levels, which is now feasible thanks to the use of AI-dedicated networks.