The original NNUE paper cites AlphaZero[0]. The architectures are different because NNUE is optimized for CPUs and uses integer quantization and a much smaller network. I don't think one could credibly claim that it would have come about if not for Google making so much noise about their neural network efforts in Go, Chess and Shogi.

0: https://github.com/asdfjkl/nnue/blob/main/nnue_en.pdf