I cannot speak to that card specifically, but I recently got an AMEX business card. I do the occasional driving for Uber (that's becoming pretty rare though), but that's it as far as anything that could be remotely considered a business. I simply applied under my own name and that was that. I used it for pretty much everything, all of my monthly expenses, in order to get the sign-up bonus.
The point being, you don't usually have to have an up and running business to get approved for business cards.
