Rypple, founded in 2008, started out with an anonymous feedback application built for the enterprise (albeit, I don't think the messaging was quite as forward as it is for this service, I think it required the manager opting in). Rypple eventually pivoted into a performance management cum next-gen performance review app, but the anonymous feedback feature is still a component. It was acquired by Salesforce.com last year.
I love the idea of anonymous feedback, it's one of the aspects of Rypple that initially attracted me to work at the company (I used to work at Rypple).
However, I'm not even sure Rypple was the first mover in the corporate anonymous feedback space, there's been quite a few similar services over the years. I think an app with just this feature, given how there's been consolidation in the HCM industry and providers now often offer a full suite of HR/performance management tools nowadays, is unlikely to achieve major success. That said, there's still a ton of small startups in the space that have similar ideas to Happiily.