Don't have a touch screen to test, but I can see that it's the right-click context menu that'd you'd get if you right-clicked on a blank spot the page.
Is this a new issue or has Opera been doing it all along?
If you goto the URL opera://flags, and search for touch, you'll see some experimental tweak you can play with.
Also, I doubt it'll help, but you can goto <]the URL opera://settings/searchPopup and disable the search popup.
Did you try disabling all your extensions? Have you changes any of the keyboard shortcuts in Opera?