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You' re right. That was a "logical failure" 
but anyway, that doesn't solve the issue.
@xiamenese, well it's strange, but this "Folder"-behavior from the Opera-Icon I have only in the symbolic view (big Icons and the name of the app). Right-clicking this Icon leads to the context-menu of a folder (new folder...information...Import from...etc.). All other Program-Icons are displaying the expected context-menu, as you mentioned (Show Package content...etc.) If I change to List-view, Opera shows also the correct context-menu. For me its strange but reproducible.
I noticed, that the Opera-Icon in the program folder (symbolic view) is not the app itself, if you (right)click on "information", it will indicate, that "Opera" is a folder...
So if you drag this Icon bona fide in your Dock, there is a sort of "folder" instead the app. It seems there is something wrong with the installation itself.
Normally a folder has its Folder-Icon, not the App-Icon.
Thank you for your specification. Your fix isn't working for me. Removed the old Dock-Icon and adding a new has no effect. Still the same issue.
Well, at least I'm not the only one... BTW: Opera Beta still the same issue.
Until Opera 60.0.3255.27 the behavior was as expected: You "minimize" Opera with the red button and it will be (active) in the dock. Click the Opera-Icon in the dock again and it will open instantly a new window. That's what I want. With the latest Opera ..... .65 a click on the (active) Opera-Icon in the dock causes... nothing. The Opera app appears in the menu bar without a new window, you have to click inconvenient "Open a new window" or "Open a new tab" in the (context)- menu.
macOs knows both behaviors: yellow button for "minimize" and red button for "minimize". If you open Safari for example and then minimize it with the red button, macOS will close the window, but not terminate the app! Click the red button again and macOs will "restore" (open) instantly a (new) window again but not the old session. That's what I meant.
Updated to the latest Opera build and noticed, that Opera will not restore to a window, when it was minimized with the red button (macOS 10.14.4).
That's annoying. I had to minimize it with the yellow button....
Anyone else?
Sorry, this won't help you, but I never had this problem with Opera. My speed dial tiles are always in the same order I wanted and never shifted. It must be some preference that not works well.