But the article never claimed it would go the same direction as the solar wind, and give no mechanic for that to happen (as the generated force is at an angle compared to it). So it may well be true it wouldn't work if you go straight out, but rather have to curve yourself outwards to avoid hitting that 0 speed reference where it doesn't interact with any particles.
The 0 speed reference frame is a usual trick. It's too difficult to do some calculations when the plasma is moving in a direction and the device is moving in another direction.
So you imagine that there is also an imaginary starships moving at a constant velocity in a constant direction. And you put an imaginary scientist doing imaginary measurements from the starship. A more serious name for the "imaginary starship" is "reference frame". All the reference frames that move at a constant speed are equivalent, they have the same laws of physics, so you can choose any of them to make the calculations.
In this case the calculations are more easy if you pick a reference frame that moves with the same speed and some direction that the solar wind (at least locally). It's only a mathematical trick, you imagine that there is an imaginary starship there just to do the calculations.
So if this device really works, it must work when you are measuring it from a imaginary starship that is moving at the same speed of the solar wind. You can't avoid the imagination. Also, all the other reference frames give the same result, but the calculation is much harder.
The advantage of using the reference frame that moves at the same speed of the solar wind is that in that reference frame the speed of the solar wind is 0. It doesn't mean that the particles doesn't move or don't interact, just that they don't move in any preferred direction. So the particles may enter the device from any direction.
If your initial setup is that the device is moving with some speed/direction that is not equal to the speed/direction of the solar wind, then in the reference frame we choose the device is initially moving in some direction with some speed.
Now, when you turn the device on, there is some kinetic energy because the device is moving and there is some energy in the electric field because the capacitor is charged. With the description in the site, the device must work even if it were a static capacitor with a fixed charge. So after a while, the ions around the device change their position and the device may start to move, but there is a maximal speed change. Initially the acceleration may be big, but then it starts to fade away. The initial energy is redistributed, part of the energy in the electric field is transformed in kinetic energy of the device, but there is only a finite amount.
When you see it from the usual reference frame, for example the one that is fixed to the Sun) the calculations are more complicated because now you have to consider the solar wind, and it's difficult to avoid some infinite amounts in the calculation of the energy. But the result must be the same that the result in the other reference frame. The device changes the speed a little and then the acceleration goes to 0.
