The reason it needs to be logged in is because Google Colab is a free service that Google provides allowing people to run code on expensive GPU servers. It doesn't cost you anything and I don't store any information from your google account when you run it.
It's just unfortunate that there is an ominous warning with no specificity. The only way I could hope to know what of my Google data is being used is to somehow read your project code.
Of course I don't expect that you have any interest in my data, but there's still a granularity problem here regarding access.
Yeah sorry. I don't know if there's anyway around it. Google colab is simply the best way to give people a chance to play the game without having to pay money or do complicated technical set up.