In practice I expect that the mechanism to be much more involved than this. Traditional holography works by capturing a fine grained picture of light intensities on a surface or even in a volume, but it doesn't capture all possible information, certainly not both the electric and magnetic fields at a given time point. It looks like the researchers use a novel holographic technique to capture more information than normally possible.
> In traditional holography, a 2D diffractive element encodes the complex amplitude of a 2D wavefront, which can be recreated by illuminating the element with a spatial reference beam. This new device can be thought of as an extension of this to an extra dimension; a three-dimensional (3D) diffractive element, which when illuminated with a reference pulse in a reference spatial mode, will reconstruct a fully volumetric optical field (2 transverse space and 1 time/longitudinal space). It is a type of reprogrammable space-time hologram.
There is a difference to Zeno's paradox, as a sibling comment suggests the impossibility. For a flying arrow we can assume that it's motion is driven by Newton's law, which is a second order differential equation for the position. Therefore you can't use the position only for initial condition to solve the equation, ie. you can't decide where the arrow travels from a snapshot of time.
However the Maxwell equations that describe classical electromagnetism are a system of first order partial differential equations in terms of electric and magnetic fields. So if you know both the electric and magnetic fields everywhere at a given time point then in theory you can predict it at every future time points.
[1] https://en.wikipedia.org/wiki/Electromagnetic_radiation#/med...