According to Wikipedia, a wave is the disturbance of a field.
A field must have a value for each point in space-time.
E.g. A water wave disturbs a body of water which is a field. This is because the displacement of water molecules is defined at each point.
E.g. A sound wave disturbs air pressure which is a field. This is because air pressure is defined at each point.
For a wave to travel through a vacuum, it must have a field to propagate through. Electromagnetic waves are said to disturb the electromagnetic field.
Vacuum fluctuations, as you describe them, cannot serve as this because they are inherently random and so are not defined at every point - hence cannot act as a field.
I agree that it is even dubious with EM waves. One way to explain it though with light is to take the corpuscular (particle) view. In which case, an energy packet can travel through a vacuum without a medium for it to travel through - just like how you could throw a rock into space and it wouldn't care that it's not moving through anything.
If you are interested, this is a very amazing explanation of EM waves: https://www.youtube.com/watch?v=FjHJ7FmV0M4.