Not sure I get your point. But contextual search only works for the search within Cliqz browser, on the address bar dropdown, on the client space. The same approach cannot be done on the (web-page SERP page, beta.cliqz.com), because from a web we have no access to the tabs opened. It could only possible via tracking and user-profiling, which is something that we do not do, or want to do.
They could, but then everyone would see them do it, and kind of the whole point is that they won't do it.
But who in their right mind would allow the Javascript code of one tab to access data in other tabs?