The buttons are clickable under the eggs, "Red" "Green" and "Blue" but they don't do anything at all, there is no progression onto a new screen, no cracking of an egg, nothing at all.
Weird.... mine works fine...
it still works for me. it should show a popup asking to name them. perhaps you have alerts disabled in your browser. or you can check the browser console (f12) and see if there's any errors. or you can try a different browser.
I hope it works!