So, I've watched this a couple times now, and first off, great song, it's been stuck in my head since i first played it. But also, i realized that there's actually a pretty deep story for those who couldn't catch on to it, so i thought i'd get into detail:
At the very start, we see that the player made it to the end of the game and triggered the end cutscene dialogue. The pink haired girl tells him that "there's something she should say" but doesn't find the courage to say it.
At 0:32 it might be tempting to think that what were seeing is a flashback of their journey, but I think what really happened is the player reset the game in slight disappointment that the pink haired girl didn't say what she wanted to, now trying to reach the end again in a strange hope that she'll somehow be able to find confidence and change her dialogue.
In the following scenes, we can see that the player asks her to come on a journey with him, and in excitement of her saying yes, he drags her across town and helps her on their way.
The girl says something easy to brush off at 1:07, stating that the player named her after "the one he loves," or more specifically, his real life crush. From here we can assume that when the player first started the game, he had the option to name the girl whatever he wanted to, and that's when he chose the name of his crush.
The next scenes show more instances where we see the girl is shy and unsure, saying in a conversation that presumably started before the cut that she isn't able to swim, and she also says she's no good at dancing when the player asks her.
Then at 1:43, the player reaches the end cutscene for the second time. When the song says "pray this time my heart will shine on through," it becomes evident that in the girls inner thoughts, she, too wants to gain the confidence to say what she wants, she even stutters twice if you pay attention to the text box, which we don't see in the original cutscene. But in the end, she hesitates and can't get it out.
At this point, the player gives up and sets the game down, and the girl instantly regrets having not said anything earlier. She tries to stop him from leaving at 2:07, but she's unable to, and can't do anything about it.
Years later, the player finds the game in his old stuff and decides to play one more time. But as you've probably read in someone else's comment, old games like this one used to run on a certain battery that lasted a long time, but when depleted can't hold save data anymore, purging the game's world forever.
The girl sees the player again, but realizes that the game is breaking and that there isn't much time left. But now, with one more chance, she rushes the player to the end of the game to trigger the cutscene for the third and final time. The girl goes to HIS house instead of waiting for him to go to hers, drags HIM through town, and helps HIM on the journey. She even finds the courage to both swim and dance with him where she couldn't before.
And when they reach the end, for the third and final time, she bares it all and cries and shows the truth, and finally, says— finally— "I love you."
