Mostly just copying from the actual TVTropes page, but I'm leaving out the ones relevant to CCC only. Unitalicized comments are mine!
And You Thought It Was a Game: He doesn't realize it until his defeat and death at the hands of the protagonist. Child Prodigy Disappeared Dad: Or rather, one he never met, since his mother used a sperm donor. Genre Savvy: In trying to keep the identity of his Servant secret, he destroyed all books and evidence that points to Francis Drake, except for one book that had too strong a seal to break. He settled for hiding it in the 2nd Floor Arena. I Don't Want to Die: He has an emotional breakdown, contrasting with his Servant. Justified, since he's only eight years old and thought it really was just a game. It's All About Me: Justified. He thinks everything is a game during Extra and doesn't realize the danger him and the others face. There's also the fact that he's really only eight years old, and children at that age are still rather self-engaged. Jerk with a Heart of Gold: According to the playable Archer, he's this. Considering that he thinks it's all a game and he's only eight years old, its very possible that he's sincere about his offer (which you cannot accept) before the Elimination Battle, rather than just being a condescending jerk. Loose Lips: LAUGHSHe tends to brag (and drop info in the process) about his Servant a lot. Justified, since he's an eight year old kid, and kids at that age tend to brag a lot. His overconfidence doesn't help either. Never My Fault: All the time. But let's face it, most people at eight years old do the same thing. Mythology Gag: He's arrogant, has quite a few female classmates fawning over him and is somehow friends with the main character, just like his Fate/stay night counterpart. Also relevant to Animus, with Shinji and ProtoGil's Master/Servant relationship. Younger Than They Look: Despite only being eight years old in real life, the avatar he uses to participate in the Grail War appears to be a teenager, because "he's bluffing, saying, 'I'm no longer a child!'"
[OU] Shinji Matou | Fate/Extra
And You Thought It Was a Game: He doesn't realize it until his defeat and death at the hands of the protagonist.
Child Prodigy
Disappeared Dad: Or rather, one he never met, since his mother used a sperm donor.
Genre Savvy: In trying to keep the identity of his Servant secret, he destroyed all books and evidence that points to Francis Drake, except for one book that had too strong a seal to break. He settled for hiding it in the 2nd Floor Arena.
I Don't Want to Die: He has an emotional breakdown, contrasting with his Servant. Justified, since he's only eight years old and thought it really was just a game.
It's All About Me: Justified. He thinks everything is a game during Extra and doesn't realize the danger him and the others face. There's also the fact that he's really only eight years old, and children at that age are still rather self-engaged.
Jerk with a Heart of Gold: According to the playable Archer, he's this. Considering that he thinks it's all a game and he's only eight years old, its very possible that he's sincere about his offer (which you cannot accept) before the Elimination Battle, rather than just being a condescending jerk.
Loose Lips:
LAUGHSHe tends to brag (and drop info in the process) about his Servant a lot. Justified, since he's an eight year old kid, and kids at that age tend to brag a lot. His overconfidence doesn't help either.Never My Fault: All the time. But let's face it, most people at eight years old do the same thing.
Mythology Gag: He's arrogant, has quite a few female classmates fawning over him and is somehow friends with the main character, just like his Fate/stay night counterpart. Also relevant to Animus, with Shinji and ProtoGil's Master/Servant relationship.
Younger Than They Look: Despite only being eight years old in real life, the avatar he uses to participate in the Grail War appears to be a teenager, because "he's bluffing, saying, 'I'm no longer a child!'"
Other things!
Leaning on the Fourth Wall: Doing things like asking Bittyroth if he's from an RPG after having materia explained to him. I mean, he's an internet/video game nerd, come on.
Tsundere: So much so that Tamamo gave him the nickname Tsunji.