This claim of "efficiency" is factually accurate but nearly meaningless as a measure of a rocket's performance. It's similar to pointing out that a car has high-efficiency LED headlights. That's great but it doesn't necessarily mean the car will have better performance or economy.
In a gas generator cycle, a small amount of fuel and oxidizer are burned to create hot, high-pressure gas which is then through a turbine. The turbine converts the energy in the gas into work, which it uses to run a fuel or oxidizer pump. Turbines have practical and theoretical limits to their efficiency; the turbine exhaust gas is cooler and lower-pressure than the entering gas but still carries about half the energy of the entering gas. Hence, 50% efficiency (roughly, typically). An electric motor is not constrained by the same thermodynamic law as the turbine. Modern brushless DC motors can turn 95% of the incoming electrical power into mechanical power, losing only 5% to waste heat.
But the overall driving metric for launch rockets isn't the efficiency of the fuel pump, it's the dollars/kg cost of payload. Things that factor into that are the efficiency of the rocket, the cost of construction, and costs of testing and operation.
Turbopumps driven by a gas-generator cycle are ubiquitous in rockets primarily because of their amazing power-to-weight ratio. The gas generator itself (burner) is basically an assembly of highly-engineered sheet metal. It's light. The turbines themselves are engineered to operate at very high temperatures and speeds and extract an ungodly amount of power for their weight. For example, the SSME high-pressure oxidizer turbopump had a power output of 23,260 hp and measured only 600 by 900 mm (24 by 35 in). That's for the turbine AND the pump. The fuel they burn has weight, but it's already on board and depletes as the rocket climbs.
Electric motors have great power-to-weight, but not as good as gas turbines. The battery is an added system that weighs the same at the end of the rocket's burn as it did at the start. A detailed analysis would probably show that a gas generator cycle would save your rocket a lot of pounds, and those saved pounds would go straight into payload capacity, bringing down the $/kg substantially.
However, the turbines used in rocket turbopumps are among the most highly-engineered, exhaustively tested, longest development time, and overall expensive parts of the entire rocket. Replacing them with high efficiency electric motors and batteries represents a substantial cost and time savings in both development and final production.
What Rutherford has done is made the engineering decision that given the specifics of their rocket - its size, anticipated volumes, their development budget and schedule - they are better off using "cheap but heavy" electric motors and batteries than a "light but expensive" gas generator and turbine. The dollars/kg increase due to losing payload to the heavier electric pump system will be more than offset by the (presumably) faster time-to-market and lower development and production costs. Pointing out that an electric motor is more efficient than a gas turbine is someone's idea of a good marketing point but it's meaningless from the standpoint of rocket performance.
