Localizing video moments based on the movement patterns of objects is an important task in video analytics. Existing video analytics systems offer two types of querying interfaces based on natural language and SQL, respectively. However, both types of interfaces have major limitations. SQL-based systems require high query specification time, whereas natural language-based systems require large training datasets to achieve satisfactory retrieval accuracy. To address these limitations, we present SketchQL, a video database management system (VDBMS) for offline, exploratory video moment retrieval that is both easy to use and generalizes well across multiple video moment datasets. To improve ease-of-use, SketchQL features a visual query interface that enables users to sketch complex visual queries through intuitive drag-and-drop actions. To improve generalizability, SketchQL operates on object-tracking primitives that are reliably extracted across various datasets using pre-trained models. We present a learned similarity search algorithm for retrieving video moments closely matching the user's visual query based on object trajectories. SketchQL trains the model on a diverse dataset generated with a novel simulator, that enhances its accuracy across a wide array of datasets and queries. We evaluate SketchQL on four real-world datasets with nine queries, demonstrating its superior usability and retrieval accuracy over state-of-the-art VDBMSs.