Not really. Godwin's law points to inadequate comparisons to Hitler and the "classic Nazis", whereas your parent points out that he supports real, alive Nazis today.
It's a not a Nazi comparison, it's stating facts. Just two days ago he recommended voting for the German fascist party AfD, in the process regurgitating white supremacist conspiracy theories.
Yes, yes, anyone you disagree with and is more right wing than 20008 Obama is a Nazi. They said the same about Meloni in Italy but that has proved to be very much not the case.