I don't know much about WolframAlpha Notebook, but that little orange "=" icon indicates that it's expecting natural language input, not Wolfram Language code. If you want to play around with neural nets, I would think you'd need Mathematica, not WolframAlpha.

When you "open a Notebook from the Neural Net Repository", are you opening it with your own local version of Mathematica or with a cloud account or with Wolfram Player or what? If you already have Mathematica, then that's the environment you want to use to play with neural nets.