Till date, Google did not allow developers to price an app for free for a limited time - if they made an app free, they could not make it a paid app again unless they removed the listing and republished it.
Reading the fine print of the Free App of the Week, we see it is being called a Google Play Content Promotion, meant for third-party publishers and entailing the use of promotional codes - though the code and its input mechanism is not visible in the case of Daniel Tiger Grr-ific Feelings. The terms of service add that "such promotional codes cannot be transferred to other users, cannot be exchanged for cash, and have no cash value."
For now, Google has not provided any details about if the new 'Free App of the Week' promotion will make its way to other sections of Google Play.In the meanwhile, Google has started posting user feedback surveys in the Google Play app, as spotted by a Reddit user. Unlike Google Reward Opinions however, answering the survey doesn't pay users in the form of Google Play credit. The survey spotted asked how satisfied the user was with the "Google Play Store's search results."