Coastline detection in remote sensing imagery is commonly formulated as a pixel-wise segmentation problem, where the final coastline is extracted from a predicted mask through post-processing. This formulation relegates coastline geometry, the primary representation used in coastal change analysis, to a secondary artifact rather than the learning objective. In practice, coastlines are defined by geomorphic proxies such as vegetation lines, dune toes, or cliff edges, rather than an instantaneous land-water boundary often used in pixel-based segmentation approaches. In this work, we revisit coastline extraction from a representation perspective and formulate the task as geometric boundary localization. We use the New Zealand Coastal Change Dataset (NZCCD) and high-resolution aerial imagery from Land Information New Zealand (LINZ) to develop CoastlineVLM-7B, a vision-language model (VLM) built on the GeoChat-7B/LLaVA-1.5 architecture that jointly performs coastline presence detection, proxy-type classification, and coastline grounding. The model directly predicts a coastline as a polyline rather than a dense segmentation mask. We evaluate CoastlineVLM-7B against segmentation baselines under strict one-pixel boundary supervision. Results show that geometry-based metrics are more suitable for assessing coastline localization quality than pixel-overlap metrics such as Intersection over Union (IoU). CoastlineVLM-7B improves global geometric alignment with reference coastlines, reducing Hausdorff distance from 37.74 m to 31.84 m and Earth Mover's Distance from 21.12 m to 17.32 m. These results indicate that output representation is a critical design choice in coastline extraction, and that geometry-oriented learning, combined with the semantic reasoning capabilities of vision-language models, aligns well with how coastlines are defined and evaluated in operational coastal monitoring.