I'm surprised that they developed a brand new time tracking tool. From my limited experience, it seems Deltek Time & Expense is the most popular time tracking application in the government / associated contractor space.
Given that there is no download link or price, I'm going to assume that 18F is not the kind of place that was going to pay top dollar for a cruddy, expensive third party service.
Like everything 18F produces, Tock is a work of the US Government and is in the public domain. There's a link to the GitHub repository in the blog post (https://github.com/18f/tock). We don't intend to launch Tock as a service, rather, it's something we made for internal use that is open for others if they find value in it.