That wasn't actually Godzilla, despite the title. His official name is Zilla and he's a mutated iguana, as opposed to Godzilla who is the mutated form of a godzillasaurus.
This one seems much more flexible, but Godzilla's stiffness has always been due in large part to the costume.
The actual design seems to follow Gojira rather than Zilla. The mouth is far less blocky and the dorsal fins are both more numerous and are back to their original shape. He also seems to have a far less hunched appearance than Zilla, shorter arms, and his neck isn't nearly as long.
If you don't mind visual spoilers you can see Godzilla's design clearly
here and
here.
They got the color right at least (i.e. not green).