Distributed deep learning has recently been attracting more attention in remote sensing (RS) applications due to the challenges posed by the increased amount of open data that are produced daily by Earth observation programs. However, the high communication costs of sending model updates among multiple nodes are a significant bottleneck for scalable distributed learning. Gradient sparsification has been validated as an effective gradient compression (GC) technique for reducing communication costs and thus accelerating the training speed. Existing state-of-the-art gradient sparsification methods are mostly based on the "larger-absolute-more-important" criterion, ignoring the importance of small gradients, which is generally observed to affect the performance. Inspired by informative representation of manifold structures from neighborhood information, we propose a simple yet effective dynamic gradient compression scheme leveraging neighborhood statistics indicator for RS image interpretation, termed RS-DGC. We first enhance the interdependence between gradients by introducing the gradient neighborhood to reduce the effect of random noise. The key component of RS-DGC is a Neighborhood Statistical Indicator (NSI), which can quantify the importance of gradients within a specified neighborhood on each node to sparsify the local gradients before gradient transmission in each iteration. Further, a layer-wise dynamic compression scheme is proposed to track the importance changes of each layer in real time. Extensive downstream tasks validate the superiority of our method in terms of intelligent interpretation of RS images. For example, we achieve an accuracy improvement of 0.51% with more than 50 times communication compression on the NWPU-RESISC45 dataset using VGG-19 network.