In complex auditory environments, the human auditory system possesses the remarkable ability to focus on a specific speaker while disregarding others. In this study, a new model named SWIM, a short-window convolution neural network (CNN) integrated with Mamba, is proposed for identifying the locus of auditory attention (left or right) from electroencephalography (EEG) signals without relying on speech envelopes. SWIM consists of two parts. The first is a short-window CNN (SW$_\text{CNN}$), which acts as a short-term EEG feature extractor and achieves a final accuracy of 84.9% in the leave-one-speaker-out setup on the widely used KUL dataset. This improvement is due to the use of an improved CNN structure, data augmentation, multitask training, and model combination. The second part, Mamba, is a sequence model first applied to auditory spatial attention decoding to leverage the long-term dependency from previous SW$_\text{CNN}$ time steps. By joint training SW$_\text{CNN}$ and Mamba, the proposed SWIM structure uses both short-term and long-term information and achieves an accuracy of 86.2%, which reduces the classification errors by a relative 31.0% compared to the previous state-of-the-art result. The source code is available at https://github.com/windowso/SWIM-ASAD.