If someone does something ritualistically, they do it in a ritualistic way: they follow the same pattern every time, as if it were part of a ritual. The adverb tells you about the manner, not the name of the thing itself. A priest might move ritualistically through a service. A nervous person might ritualistically check the lock three times. A team might ritualistically touch a sign on the way onto the field. Though actually, this word can sound a bit stiff or critical, as if you are saying the person is stuck in the pattern. In simple talk, people often just say “like a ritual” instead.