Because You Were Nice to Me: Derpy ends up taking Trixie's side in the seventh contest because Trixie didn't gawk or make fun of her eyes when they first met.
The Chessmaster: Twilight Sparkle seems to outdo even Celestia in this fic. She places Trixie's scry spell on a photo in Trixie's bag to listen in on her, faking Stalker With a Crush behaviour and invokingLoophole Abuse in order to test Trixie's determination and compassion for her. This shows up even earlier when she actually uses her magic at full power for once in the third trial in order to gain the rights to spend time with Trixie through more Loophole Abuse, so she can learn more about her and finally become friends with her.
Florence Nightingale Effect: Derpy and Fluttershy became a couple after the former crashed into the latter's cottage and had to be nursed back to health.
Relationship Upgrade: Derpy and Fluttershy had this before the story began, as did Rainbow Dash and Pinkie Pie. By the end of the story, Twilight and Trixie have gotten here as well.
Serious Business: Titles are prestigious enough that there are formal rules regarding how they are transferred and competed for, and seventy unicorns end up competing for "Great and Powerful" in the tournament. And the subsequent victor will spend the rest of their life stalked by challengers. Said rules have a few useful loopholes to avoid most of the hassle, though.
Walking the Earth: Trixie does this near the end of the story to become a more powerful unicorn. By the end of the fic, she has to do it again because it's a requirement of winning the title of Great and Powerful. Fortunately, Twilight pulls her Loophole AbusingXanatos Gambit at this point.