Should Kirchhoff's Law be changed to account for information removal?
Kirchhoff's laws are a huge simplification of Maxwell's equations under some very specific assumptions (lumped elements, quasi-static fields, etc.).

Hence they are part of classical physics, as Maxwell's equations are.

Relativity and quantum mechanics are not part of classical physics, so you shouldn't expect that relativistic effects could, in any sense, be modeled by KVL and KCL.

EDIT (to answer part of a comment)

You say:


  I wonder if some adjustment should be made, much like Einstein did for physics (approaching 0.5c)...


This hasn't got much sense, and I'll try to explain why.

Einstein's theory (special relativity) added "adjustments" to what, at the time, was the most accurate theory available (Newtonian mechanics), and took another extremely accurate theory (Maxwell's equations) as foundational (he postulated that Maxwell's equations were invariant in any inertial frame of reference, IIRC). 

What would be the point to refine KVL and KCL? They are already much more inaccurate than Maxwell's equations, as a general theory. Any relativistic adjustment would be a drop in the ocean. Once you get the frequency sufficiently high, radiative effects and transmission line behavior (both predictable using classical Maxwell's theory) are enough to swamp any possible relativistic correction.