Is there a gap amplification type of result for the Graph Isomorphism Problem?
I do not know if such a thing could exist or not. But it is interesting (and perhaps timely) to note that such a "gap amplification" would likely imply a quasipolynomial time algorithm for graph isomorphism (different than the recently announced one)

In this paper, an approximation algorithm is given for the "MAX-PGI" problem of maximizing matched pairs of edges/non-edges; if we reduce from GI to "Gap-MAX-PGI", then we can approximate to distinguish which side of the gap we are on.

So, I think Dinur's proof of the PCP theorem is unlikely to be directly generalizable to such a "gap amplifier", given the hurdles that would have to be overcome.