Spatiotemporal information is at the core of diverse sensory processing and computational tasks. Feed-forward spiking neural networks can be used to solve these tasks while offering potential benefits in terms of energy efficiency by computing event-based. However, they have trouble decoding temporal information with high accuracy. Thus, they commonly resort to recurrence or delays to enhance their temporal computing ability which, however, bring downsides in terms of hardware-efficiency. In the brain, dendrites are computational powerhouses that just recently started to be acknowledged in such machine learning systems. In this work, we focus on a sequence detection mechanism present in branches of dendrites and translate it into a novel type of neural network by introducing a dendrocentric neural network, DendroNN. DendroNNs identify unique incoming spike sequences as spatiotemporal features. This work further introduces a rewiring phase to train the non-differentiable spike sequences without the use of gradients. During the rewiring, the network memorizes frequently occurring sequences and additionally discards those that do not contribute any discriminative information. The networks display competitive accuracies across various event-based time series datasets. We also propose an asynchronous digital hardware architecture using a time-wheel mechanism that builds on the event-driven design of DendroNNs, eliminating per-step global updates typical of delay- or recurrence-based models. By leveraging a DendroNN's dynamic and static sparsity along with intrinsic quantization, it achieves up to 4x higher efficiency than state-of-the-art neuromorphic hardware at comparable accuracy on the same audio classification task, demonstrating its suitability for spatiotemporal event-based computing. This work offers a novel approach to low-power spatiotemporal processing on event-driven hardware.