“Let’s Play” has been a common part of gaming vernacular for many years now. So it may seem obvious that any attempts to trademark the phrase would fail. However, the application actually failed because of an existing trademark on “Let’z Play."
This is actually the second time that the patent has failed for reason. The letter says:
Sony has until the end of June to appeal the decision. In order to be approved, they would need to prove that their new trademark is sufficiently different from the existing trademark.
Users on NeoGAF have observed that this new trademark may not be an attempt by Sony to prevent average gamers from uploading Let’s Play videos to YouTube or Twitch, but rather would exist to prevent Microsoft or Nintendo from using those words in any official branding.
