Spiking neural networks (SNN) are a promising approach for low-power edge AI (artificial intelligence), especially when run on dedicated neuromorphic hardware. In this work we set up a SNN in TensorFlow, directly train it in a supervised manner with backpropagation through time (BPTT) and surrogate gradients, and compare it with traditional neural networks, based on convolutional neural networks (CNN) and long-short term memory (LSTM) cells, for radar-based hand-gesture recognition. We demonstrate that a small SNN with only 30 hidden leaky integrate-and-fire (LIF) neurons and threshold encoding can achieve an accuracy of 98.1%. With the more complex adaptive LIF neuron, the activity can be reduced by up to 37.9% without significant loss in accuracy. A comparison to traditional LSTM-networks shows the superiority of the SNN in terms of accuracy and computation cost, indicating that they are a considerable alternative to LSTM-based approaches.