Accidental Misnaming: The stallion met in Chapter 11 at the stadium has a name tag labeling his name as "Hymie", saying that the pony in charge of making them had looked too busy to hear his name right, and due to the tag, everypony calls him that before he can properly introduce himself. (For the Record, his real Name is Hermos.)
Adult Fear: The Children (and Luna) on Nightmare Night being surrounded by Brainwashed and Crazy Griffins that want to eat them. Luna could handle them, but considering how they possess a Power that could potentially harm her...
Try imagining your loved one frozen in place, right in the way of an attack heading right towards them. then imagined said loved one falling when the ground they were standing on collapses out from under them from said attack. This is what Celestia and Luna ended up experiencing with each other, respectfully.
Affectionate Nickname: Luna constantly calls and refers to Yugi as "Little Game". Unlike Rainbow Dash's nickname of "Sheep Boy", Yugi likes this nickname and doesn't mind it if she calls him that. his In-Series Nickname of "Yug" is used by Shining Armor.
Allergic to Evil: If Yugi touches An Orichalcos Stone, it will physically hurt him. When Twilight shows him one that fell off a griffin, she uses her magic to pick it up and places it in Yugi's hoof when he wants a closer look. It burns his hoof and he stomps it into dust as retaliation.
Anger Born of Worry: Yugi blowing his top at Pinkie during Luna and the Little Game, is most likely this, though the anger is more so out of concern for Luna's self-esteem.
Amplifier Artifact: The Elements of Harmony and their higher counterparts naturally fall here.
The Element of Hope, however, takes this Up to Eleven; if its true power is unlocked and used properly, it can supercharge the other Elements.
Amnesiac Hero: Yugi, as upon the arrival to Equestria. All of his memories before he arrived have been erased, save for his name (and even in the beginning, he wasn't sure if it was his own name to begin with).
Wistful Amnesia: He's very much aware that something feels missing when it comes to his friendships, if only as a passing feeling.
Been There, Shaped History: In-Universe example: Yugi is there for certain key events that happen in Seasons 2 and 3, and and is also the cause of certain events, whether he directly causes it or he indirectly helps.
Call Back: There are some call backs to the anime and the manga for Yu-Gi-Oh!, the main one is a mechanic from the Manga where Yugi plays various games with opponents. Justified that the game of Duel Monsters does not exist in Equestria. Not yet, anyways.
The idea that Yugi suggested to Shining Armor of using a Jigsaw Puzzle to tell Cadence a message is a reference to episode 10 of Season Zero, for an example.
Chekhov's Gunman: Guiding Wings appears earlier before her debut chapter—she comes to ponyville and asks Yugi for directions to the town hall, who quickly tells her the directions and runs off to join the Mane 5 in finding Applejack. She otherwise doesn't pop up until after the preceding chapters' events.
Clingy MacGuffin: The Element of Hope is this for Yugi, as it cannot be removed by anypony except by his own hoof, and even then, if he discards it, it'll simply return to him in some way or another. It's lampshaded in Chapter 9, by Princess Luna and a doctor, the latter saying they've even tried a buzzsaw to get it off, and it still didn't budge.
Crosses over with Noodle Incident in-story (as we don't get all of the details), during their conversation in Magic Lessons and The Caller, Yugi brings up the time when he was building his own home on a Tuesday to Twilight as a point on why he's hesitant to have her as his mentor in teaching him magic.
Yugi: ...Remember that one Tuesday, when I was trying to build my house?
Desperately Looking for a Purpose in Life: In addition to losing his memories, Yugi does not have a Cutie Mark and has no idea what his purpose and special talent is. He downplays it, as he'd rather it not get in the way of anything important, but he does long to know what his purpose is, even if its linked to his memory loss.
Doorstopper: confirmed by by the Author herself that the story will be this. For an example? The story is to be expected to have 95 to 110 chapters by the time it reaches its end—and that's counting the extended parts to a chapter. It's because of this estimated length that the author takes their time updating the story (and revising any early chapters) and often has to take a hiatus in order to regain motivation.
"Yawning and curling up, he fell asleep, figuring a nap was well needed to get the troubles off his mind. After all, Applejack said she would be fine. Nothing could go wrong, could it?" ((The beginning of the very next Chapter)) "Sometimes Yugi wished he didn't have such a good sense of how things would turn out."
Guardian Entity: Guiding Wings, AKA Guardian Eatos, just like in her canon source. She's also this to Princess Celestia and Luna, albeit more out of their friendship and loyal servitude, the latter being detailed in Chapter 20.
Hope Springs Eternal: The Lost Element (AKA: the Element Of Hope) is a Physical representation of this: It was made by its first wielder during a time in Equestria when things were at its bleakest— because he refused to give up in the face of what seemed to be an endless despair, his faith in his friends, and in turn, the faith his friends had in him solidified into the Element Of Hope. As long as there's Hope within its spirit, its magic never falters.
Mundane Utility / Utility Magic: Once Yugi gains the possession of the Element of Hope, his main use of it (aside from crisis situations) is to take advantage of its ability that allows him to preform Basic Unicorn Magic, Such as making things levitate and teleportation spells. So far, he uses that magic to write letters, send them, and carry things more easily when he can use it.
Multicolored Mane: par for the course for Yugi, albeit it's more fluffed and out of shape. as this trope is also common in Equestria, it isn't seen completely out of the ordinary.
Pony Cannonball: Yugi, unfortunately, becomes the test dummy to the latest venture in Cutie Mark Crusading, resulting in him being shot out of a cannon and into the Canterlot Castle.
This lovely gem from Part one of The Lost Element:
Princess Luna: ...And here, we have what we call the "timepieces" of our Equestrian Armory. Our sister tells us that these Bronze-made suits are from our "Baroque" periods in Canterlot History. That, of course, prompts the saying, "If it isn't 'Baroque',Do not fix it!"
My Significance Sense Is Tingling: Pinkie Pie's Pinkie Sense again falls here, but as it turns out, Yugi has something similar to her sense as well. One sign of this sense pops up in Chapter 11—His tail shakes and fluffs up until it looks like a bunny's tail right before he (literally) runs into Guiding Wings.
Snowed-In: Most of the "Lost Element" chapters have this in for Canterlot.
A Storm Is Coming/Hostile Weather: Twice, as of currently: one being a snowstorm over Canterlot That lead to the appearance of Red Eyes Black Dragon in Canterlot and Yugi getting the Element Of Hope, and the other being a huge thunderstorm spreading all over Equestria, with Guiding Wings showing up in Cloudsdale.
Summon Magic: The magic that Twilight uses (twice) in the Save the Prince chapters is this. However, the reason why it doesn't work as planned the first time is that the summoning spell is specifically meant to summon monsters for combat, not objects like the muffin that Twilight summons the first time she uses the spell. It is directly implied that the spell is the same magic used to summon monsters to the field in Yugi's universe, and that she picked it up from Yami (albeit he told her NOT to even try it) himself.
Tempting Fate: "He was having a very bad day, but he looked on the bright side. It wasn't like it was to get worse." Cue Sombra. This was inwardly lampshaded by Timaeus when he appears.
Win to Exit: The only way for the girls and Yugi to escape the role-playing game they were put into by Red Eyes is if they defeat the Sorceress Dark Comet and Save the Prince she has captive.
Year Inside, Hour Outside / Narnia Time: The flow of time between Yugi's world, The Beasts' Domain, and the Mane Six's world is this. While years pass by in Equestria, months pass by in the human world, with half of an Equestrian year being half of a month for Yugi's universe.