I'm getting a little bit tired of the never ending fascination with QM 'weirdness', because it seems to me that it tries to see everything as 'weird' simply because it is 'quantum', with the danger that that it makes people blind to what might be explainable by more intuitive means.
In this case I think we see an illustration of the fact that the notion of a particle as a mathematical point in space - something with zero dimensions - is an abstraction; an approximation that works well enough because we can't in that much detail any way, and it makes the equations so much easier. We have always known, somewhere, that this is not true - things like the mysterious wavefunction that mysteriously collapses as soon as we measure it is a big hint, I would say. As explanations go, that one has always sounded a bit strained - hopefully we will be able to handle the maths of a better model in the not too remote future.
A more likely scenario, in my view, is that what we call particles is something more distributed in space, and that somewhere in that 'distributed particle' we can explain how a particle can travel through several paths at once. I mean, it isn't even an altogether new observation - the famous electron diffraction experiment shows something similar.