That is indeed what should happen. At least if you open the item in the View Pane or a Document Window. I personally don’t use the read/unread status, so I basically ignore it… But I just tested to be sure, and opening in an external application doesn’t change the status.
So it won’t change automatically if you
(a) open the item with an external application (meaning: Data/Right Click > Open with… or you set Double-click open documents externally in the preferences), or if you
(b) click the item while you have set your window to View > Preview > None.
What exactly is the problem? Are you confused about the number of unread items? Does the status really not change? Or can’t you figure out how to manually change the status?
DEVONthink assigns every new item in you database the status “Unread”. It seems all the unread items are from your Global Inbox… Where you have an indexed folder called “Inbox”. Did you just index it? Then all the files in it are new to DEVONthink, and thus, unread.
You can manually change the read/unread status in several ways. It is visually indicated with a circle/dot, which you can click to toggle. In the inspector Info > Generic:
In the window toolbar:
You can show it as a column in the item list, if you like. Choose View > List Colums > Flag. Here you can also click it to toggle.
Or you can right-click one or more items and choose Mark > As Unread (Checkmark = Unread. Click and the checkmark goes away = Read). This is the easiest way to change the status of multiple items.
The same command is available in the Menu bar: Data > Mark > As Unread (which means you can assign it a keyboard shortcut, if you wish).
Now, I don’t know if you have any weird smart rule set up that changes the read status… but I suspect not.
Hope this helps you 
I actually agree that for this particular topic, it is not so easy to search the built in Help. It is much easier if you download the PDF manual and use DEVONthink’s search inspector. You might search for:

I prefer the PDF in general, because I can make highlights and notes, easily link to specific places, or use the Table of Contents to navigate. Highly recommended 