There were some comments in the larger thread over at r/politics that mentioned the fact that Trump must acknowledge that his lawyer was acting on behalf of him for the contract to be valid because he didn't sign it.

Because his current position is that the contract never existed, that would mean that his lawyer didn't notify him of it, which would mean that his lawyer's signature couldn't be used as proof of his consent, which would render the contract null and void.

The complaint itself is here: http://cdn.cnn.com/cnn/2018/images/03/06/filed.complaint.pdf

It's much more clear when you read the document. They are forcing him to either acknowledge that he entered into the contract, or possibly get more money out of him by making a new contract for more money.