What is the ruling on supplicating with the words: "O Allah, do not make us among those whose efforts are misguided in the worldly life, while they imagine that they are doing good deeds," and does this contradict the verse that speaks about those who do not worship Allah?

There is no harm in the aforementioned supplication. The noble verse: "Say, 'Shall we inform you of the greatest losers in [their] deeds?'" is general and applies to everyone who takes a path, thinking they are guided, when they are not. This includes the Haruriyyah (a sub-sect of Khawarij), Jews, Christians, and others—everyone who worships Allah in a way that is not pleasing to Him, yet believes they are right and their deeds are accepted, when in fact they are mistaken and their deeds are rejected.