I would use an app like this if I was sending sensitive or personal information that I only wanted a specific person to see. Requiring that person to respond would let the user know that they are the ones viewing the message at a certain time. This can have many benefits in the growing demand for privacy.
Many Apps already use features to promote immediate replies, such as Facebook's 'message read' function. Sometimes you just want to check a message and reply at a better time, and functions that promote replies lead to more problems than they're worth. People feel like you're ignoring them if you don't reply instantly, when that isn't always the case. I will use social media as and when I like it, not when some app company thinks I should.
I'm not a huge fan of apps because they all seem to either cost a lot of money or they try to sell you something while you're in the app. The ads, the in app purchases, it just ruins it for me. The Slingshot app sounds terrible and I have my doubts I would even download it to check it out.
I would not be happy with an app that forces you to send a message in order to see a message. It sounds annoying, silly and even a little complicated. I can see why they think it will help people feel less judged and more creative, but I don't think things will actually work out that way.