It's a perpetual motion machine.

If you have an engine that produces one newton per 10W of input power, then move it 20 meters a second, you can extract 20W from this.

At 200m/s, 200W. Leaving 10 (or 190W) of free energy output after you subtract the first.

Agreed. Let's make this a little more rigorous.

Suppose that the device has a mass of X kg and produces A Newtons per Watt of power, with a power of 1 Watt. Turn it on. It is consuming 1 Joule / sec and producing A Newtons, so the device is (in free space) accelerated at A/X m/sec^2 and (after N seconds) is moving at NA/X m/sec, giving it a kinetic energy (1/2 mv^2) of (X/2) * (NA/X)**2 = N^2 A^2 / 2X Joules for an expenditure of N Joules.

When N^2 A^2 / 2X is >= N you break even (ignoring losses), i.e., when N >= 2 X / A^2. If X is 5 kg and A is ~ 5 x 10^-6 N/W (typical numbers claimed), then N needs to be ~ 4 x 10^11 seconds (12,675 years) and the device velocity will be 400 km/sec. Clearly, energy is being created and (at this relatively low velocity, 0.0013c) special relativity will not change this situation.

Whether this actually works and, if it did, whether it would be a practical means of creating energy are, of course, rather different questions.