User identification enables secure access to data and machines in smart factories. Compared with other modalities, ECG-based user identification is rising due to its intrinsic liveness proof and invulnerability to spoofing without contact. On the other hand, as new employees are registered at the factory, the ECG-based user identification system needs to be updated based on the new coming data. This scenario can be defined as an online class-incremental learning (O-CIL) problem. By exploiting hardware-software co- design, this work presents a Scalable QR-decomposition-based extreme learning machine (S-QRD-ELM) engine that can effectively and efficiently support O-CIL for ECG-based user identification. At the software level, we apply the concept of “the others” class and inversion-free QR-decomposition (QRD) recursive least squares to the S-QRD-ELM. This makes S-QRD-ELM achieve 79.7% higher accuracy in the O-CIL scenario compared with the neural network trained with back-propagation (BP-NN). At the hardware level, a one-dimensional diagonally-mapped linear array (1D-DMLA) is proposed to efficiently compute the QRD and back-substitution (BS) operations inside the S-QRD-ELM, reducing 98.5% of the silicon area. Moreover, the integrated processing element (PE) design with the unified COordinate Rotation DIgital Computer (u-CORDIC) further reduces 15.3% of the area and 22.4% of the power consumption. This engine is fabricated in 40nm CMOS technology with a $1.33\times 1.33$ mm2 die area. The chip achieves $0.02\mu \text{J}$ /sample and $2.47\mu \text{J}$ /sample inferencing and learning energy efficiency, respectively, which is $6.4\times$ and $28.5\times$ than the state-of-the-art. To the best of our knowledge, the proposed highly energy-efficient S-QRD-ELM engine is the first chip to meet the requirements of O-CIL for ECG-based user identification.