The 1000V/m only applies for the short distances (i.e., SPD connection distances) under discussion. The high voltage is the result of the high impedance of the high frequency components. These high frequencies are "impeded" (converted to heat) and diminish in amplitude as the pulse travels along the wire. As the pulse is stripped of its higher frequencies, the impedance (due to inductance) will be less...and the resultant voltage drop will be less. To explicitly answer the OPs question, if you continued to measure the voltage drop over 1 meter intervals, it would continually diminish. It will not remain 1000 V/m. In the limit (if all frequency components are stripped), the voltage drop would be whatever DC current remained multiplied by the wire's resistance (i.e.., V = IR).
The main point of the example is to illustrate that the choice of an SPD must consider the voltage impressed across the connections (a function of connection length) as well as the voltage across the SPD device itself. For example, if equipment needs to be protected at 700V, one might acquire an SPD that triggers at 500V and think that's enough. But if the connection wires...due simply to the inductance in the wire...contribute an impedance that results in 500V of drop, then the NET delta is 1000V. That is, the SPD that triggers at 500V (across the SPD), won't trigger until the device under protection sees 1000V. And if that device fries at 700V....it's gone.
Big point: Wires have inductance. In daily work dealing with household current, this inductance is negligible or factored into the real resistance. Rapid pulse spikes (e.g., from lightning) create very high frequency components. As frequency goes up, inductance that is otherwise negligible begins to be felt. Now that wire that is a "short circuit" in daily life becomes a very high impedance when that lightning surge runs through it. Low impedance path in daily life becomes high impedance path (read also, high voltage delta) during lightning.
