I did generate that screenshot as I am not in the beta for this - I don't think many outside of GitHub are. However, this is exactly how GitLab does it and I would be _really_ surprised if this is not almost exactly how it's implemented. There is almost no other reasonable way to do it.

You can't select the repository format based on the first thing pushed to it, because both sides have to be initiated before a transfer can happen.

So you either start the project on the server and then clone an almost empty repository to start working (which I think is rare) - in which case you need to choose the format like this.

Or you initialize it locally and start your project and then push it to GitHub at some point, in which case you need to initialize a server side version that matches the format to push it to. There is no "initialize a new thing on push" and there never has been.