Twilight is likely losing because she memorized only the Sicilian Defense, and it's variations, and no other opening. Also, knowing Twilight, she would be frustrated by Pinkie Pie making moves that aren't considered the best, and either focus too much on one thing or over thinking it.
Based on what I see, it appears that Pinkie Pie has four pawns, two rooks, and one knight. Twilight has two pawns and one knight. Given what I see, unless Pinkie makes blunder after blunder, Pinkie Pie will win. The reason is that in two turns, Pinkie will be able to move her pawn across the board and make it a Queen (I guess it's actually a Prince in this game, but I'm using the chess term Queen in this case). After Twilight moves her Princess up to attack the Knight, Pinkie could just attack Twilight's Knight with her pawn, and let Twilight take her Knight. After that, Pinkie will be able to move her pawn to the end of the board. Twilight's Princess is too far away to help, so there is nothing that Twilight can do to stop it.
Not sure if it applies to chess, but a practiced strategy can fall apart if your opponent doesn't respond as you expect.
Very interesting book called "How to Lose A Battle", which details military actions where one side seemed to have all the advantages, and lost. One phenomenom it details is the "Dance of Defeat". One side has a strategy that requires an opponent respond in a specific manner. But opponents don't always do what you want them to. And staying committed to a plan, even a good plan, when circumstances have passed it by is not likely to win anything.
If Twilight is too much "By the Book", then a loopy bizarre playstyle may put whatever clever gambit she had arranged in the toilet. Aaaand, there's Pinkie Pie.
Wait... why are they playing on a 8 x 7 board? And why is Twilight so worried when she's only in check from a knight in an open space? Plus, Pinkie just has slightly more pawns than Twilight, so there's not a HUGE material disadvantage... O_o
1. It is an 8x8 board, it's just hard to see one of the columns. 2. Pinkie has a much better position, assuming that the pegasi are knights. I assume the guards are rooks, which would mean that Twilight needs to move her king forwards to prevent check next turn. Pinkie would likely move her pawn towards advancement, capturing the knight at the same time. Twilight's best move would be to capture Pinkie's knight. Pinkie advances her pawn (likely to queen), and Twilight is now unable to move backwards. At that point, it's just a matter of time.
I mean, I'm sure a much better player than I might be able to save this game, but it looks like Twilight's had it.
Think that the problem is that Twilight Sparkle isn't good with playing with a timer. Fast chess require that you keep the eye on the board. How much time she lost writing and reading her notes. She doesn't seem to handle well the pressure. I think that she won't find the good strategy in time. She is doomed by the clock.