To mark a message on the Chats page as read, you have two options.
First option is to hover over the highlighted customer on the Chats list. Once hovering over, a mail icon should appear to the right of the customer's name. Click on the mail icon to mark the message as read.
The second option is to click on the conversation with the customer to open their customer profile. At the top right of the screen, there will be a mail icon above the customer profile. Clicking on the mail icon will mark the message as read.
Here is a quick video showing how to mark a message as read: