Hasbro is promoting the 75th anniversary edition of the Monopoly board game. Not only does it have a new circular game board, it contains clips of popular songs from artists such as Beyonce and Rihanna. So, how did they do that? Hasbro had to secure permission to use the underlying songs from the music publishers that own the song copyrights. To be able to use the actual recording by Beyonce and other artists, a master use license had to be secured from each record label that owned the master recording.
Use of the underlying song may have been treated as a mechanical license as this usage does constitute a mechanical reproduction. Because less than the whole song will be reproduced, the rate will most likely be less than the full statutory rate which is currently 9.1 cents per song. Hasbro is most likely paying an upfront advance of royalties along with a penny rate for each game sold.
The master rights owner, typically the record label, is probably being paid on a most favored nations basis with the song copyright owner. That means, both the publisher and record label are getting paid the same amount.
Could this use constitute a public performance under the U.S. Copyright Act? Most likely a public performance issue would only come up if there is a public game or tournament involving the game where the music clips will be heard in "public." Playing the game at home with your friends, does not constitute a public performance.
Licensing third-party rights is nothing new to Hasbro. There are many different "branded editions" of Monopoly and other games in the marketplace.