This is also applicable to the Minecraft Legends page, and likely other pages. It depends on whether the user has a license to the game of the 'Play' page they are viewing. If they do not, then at least the Windows logo is present. On the Minecraft Legends page, the editions of Minecraft Legends can be seen. On the Minecraft Dungeons page, the editions of Minecraft: Java Edition and Minecraft: Bedrock Edition can be seen. The entire Dungeons page is full of information about those two games instead of Dungeons, which is its own issue which is likely already being tracked here.

I only had a license to Dungeons and Legends through a subscription to Xbox Game Pass for PC but own a license to Minecraft: Java Edition and Minecraft: Bedrock Edition.