>>280567381The thing to remember about the adaptation, as the other anon pointed out, is that it's essentially the singular line through the UBW route that results in Shirou succeeding. It's the course of events where he makes the exact right choices and fate conspires to see him through.
>LancerHe doesn't exactly enjoy killing innocents, but he did come for him after he realized Shirou was revived. His heart wasn't exactly in it when he showed up to finish him off, and then Saber appeared to protect Shirou and Lancer's orders to scout and then leave kicked in.
>ArcherArcher wanted to make Shirou suffer out of spite for himself. He wanted catharsis for his own past foolish decisions. Immediately killing Shirou wouldn't be the same as making him see the error of his ways before drowning in despair and dying.
>RiderThroughout the VN, you see that Rider isn't taking things too seriously because she really only wants to act for Sakura's sake. She rarely goes all-out and it's not really until the final route she really does everything she can.
>GilgameshGilgamesh is basically the anti-plot armor man. He will do everything he can to sabotage himself out of hubris. He has an insanely haughty disposition and loathes going out of his way to kill those he sees as beneath him. He'd rather humble them and let them try to reach for him again later if they can.
The VN definitely conveys all of this better, I will give you that.