Ok so this happened to me (using a macbook air) and I just figured it out but it requires an Apple TV or other device with larger screen, but basically you need to connect to the other device using AirPlay (open up System Preferences --> Display --> Airplay Display). Then once you've shared your laptop screen with the Apple TV, change "Optimize for" to the name of your apple TV. This will shrink the windows so you can access the "place order" button.
And, what is solution for those of us, not on the dark side that are using Windows, but have exactly the same problem?????