This does feel a bit weird - short-term rental of petting animals? I'm worried about mishandling, animal cruelty and the whole concept - pets form an attachment with you, doing it as a short-term rental isn't an acceptable way of building a relationship...
From the article "You will have a chance to adopt the Kittens! YES, IT’S TRUE! For more information, please chat with the shelter representative that will be assisting with kitten wrangling!"
All kittens come with a shelter representative who will presumably keep an eye on you and the kitten.