Reservoir computing (RC) is a special recurrent neural network which consists of a fixed high dimensional feature mapping and trained readout weights. In this paper, we introduce a new RC structure for multiple-input, multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) symbol detection, namely windowed echo state network (WESN). The theoretical analysis shows that adding buffers in input layers can bring an enhanced short-term memory (STM) to the underlying neural network. Furthermore, a unified training framework is developed for the WESN MIMO-OFDM symbol detector using both comb and scattered pilot patterns that are compatible with the structure adopted in 3GPP LTE/LTE-Advanced systems. Complexity analysis suggests the advantages of WESN based symbol detector over state-of-the-art symbol detectors such as the linear minimum mean square error (LMMSE) detection and the sphere decoder, when the system is employed with a large number of OFDM sub-carriers. Numerical evaluations illustrate the advantage of the introduced WESN-based symbol detector and demonstrate that the improvement of STM can significantly improve symbol detection performance as well as effectively mitigate model mismatch effects compared to existing methods.