Reservoir computing (RC) is a special neural network which consists of a fixed high dimensional feature mapping and trained readout weights. In this paper, we consider a new RC structure for MIMO-OFDM symbol detection, namely windowed echo state network (WESN). It is introduced by adding buffers in input layers which brings an enhanced short-term memory (STM) of the underlying neural network through our theoretical proof. A unified training framework is developed for the WESN MIMO-OFDM symbol detector using both comb and scattered pilot patterns, where the utilized pilots are compatible with the structure adopted in 3GPP LTE/LTE-Advanced systems. Complexity analysis reveals the advantages of the WESN based symbol detector over the state-of-the-art symbol detectors such as the linear the 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 corroborate that the improvement of the STM introduced by the WESN can significantly improve the symbol detection performance as well as effectively mitigate model mismatch effects as opposed to existing methods.