6DoF object pose estimation is fundamental to robotic grasp tasks. While recent learning-based methods achieve high accuracy, their computational demands hinder deployment on resource-constrained mobile platforms. In this work, we revisit the classical keypoint matching paradigm and propose GMatch, a lightweight, geometry-constrained keypoint matcher that can run efficiently on embedded CPU-only platforms. GMatch works with keypoint descriptors and it uses a set of geometric constraints to establishes inherent ambiguities between features extracted by descriptors, thus giving a globally consistent correspondences from which 6DoF pose can be easily solved. We benchmark GMatch on the HOPE and YCB-Video datasets, where our method beats existing keypoint matchers (both feature-based and geometry-based) among three commonly used descriptors and approaches the SOTA zero-shot method on texture-rich objects with much more humble devices. The method is further deployed on a LoCoBot mobile manipulator, enabling a one-shot grasp pipeline that demonstrates high task success rates in real-world experiments. In a word, by its lightweight and white-box nature, GMatch offers a practical solution for resource-limited robotic systems, and although currently bottlenecked by descriptor quality, the framework presents a promising direction towards robust yet efficient pose estimation. Code will be released soon under Mozilla Public License.