To change the passage from third-person limited to third-person omniscient, the narrator's perspective needs to be expanded. In the third person omniscient, the narrator is all-knowing and can provide insight and information about the thoughts and feelings of all the characters. To achieve this, the narrator needs to be given an expanded perspective that includes the thoughts and feelings of both Diego and Whitney.
Revised passage:
Diego looked over the edge. He thought about how far the ground was. The wind gusted. Whitney turned to him and said, "It's beautiful up here, huh?" Diego could not think about beauty. All he could think about was not falling off the edge. He said, "Yeah, Whitney, it really is beautiful. Hey, how long do you want to stay up here?"
Diego wondered why Whitney was so carefree. Didn't she realize the danger they were in? He wished he could calm his racing heart and enjoy the stunning scenery, but all he saw was the possibility of a deadly fall. Meanwhile, Whitney's thoughts were of a different nature. She felt liberated and invigorated as if she had escaped the confines of the world below. When Diego asked how long they wanted to stay up there, Whitney laughed at the absurdity of the question. She felt like they could stay up there forever and never need anything else. This scenario was far from Diego's mind though. He could only think of slipping off the edge and failing to get back up.