Spike extraction by blind source separation (BSS) algorithms can successfully extract physiologically meaningful information from the sEMG signal, as they are able to identify motor unit (MU) discharges involved in muscle contractions. However, BSS approaches are currently restricted to isometric contractions, limiting their applicability in real-world scenarios. We present a strategy to track MUs across different dynamic hand gestures using adaptive independent component analysis (ICA): first, a pool of MUs is identified during isometric contractions, and the decomposition parameters are stored; during dynamic gestures, the decomposition parameters are updated online in an unsupervised fashion, yielding the refined MUs; then, a Pan-Tompkins-inspired algorithm detects the spikes in each MUs; finally, the identified spikes are fed to a classifier to recognize the gesture. We validate our approach on a 4-subject, 7-gesture + rest dataset collected with our custom 16-channel dry sEMG armband, achieving an average balanced accuracy of 85.58±14.91% and macro-F1 score of 85.86±14.48%. We deploy our solution onto GAP9, a parallel ultra-low-power microcontroller specialized for computation-intensive linear algebra applications at the edge, obtaining an energy consumption of 4.72 mJ @ 240 MHz and a latency of 121.3 ms for each 200 ms-long window of sEMG signal.