Yes, it improves efficiency under certain circumstances. This approach doesn't appear help if you wanted to set a record for world's most efficient water electrolyzer. But it does offer an efficiency improvement at industrially relevant (high) current densities. A lot of reported efficiency advances are relevant to setting records in the laboratory, but would be irrelevant to industry for various reasons. This appears to be the rarer case of the opposite limitation: not useful for setting new efficiency records in the laboratory, but potentially useful for improving industrial devices.

If you look at the full paper through sci-hub [1], it's an efficiency improvement specifically at higher current densities. In the left hand side of Figure 1, the magnetic/non-magnetic curves are indistinguishable at very low current densities. Those low current densities also have the lowest overvoltage and highest efficiency per gram of H2 produced. But for an industrially optimized device you want to push production rates higher for a given electrode area, which requires more current density, which also requires more voltage. Higher current density implies higher energy wastage since the voltage has to go up too.

The voltage increase with higher current density rises more slowly in the presence of a magnetic field. By the time current density reaches 50 mA/cm^-2, the setup with the magnetic field needs several millivolts less than the control setup without a magnetic field.

[1] https://sci-hub.tw/10.1038/s41560-019-0404-4