Well, moving the vines are the main mechanic of the game since it's a puzzle game about moving vines! ;)
I commented on your youtube video, but I'll say it here as well.
The game is made to be played with a controller, and the keyboard and mouse controls were added almost as an afterthought close to the end of the project. That's why the in-game hints only say which buttons to press for a controller.
If you want to play with keyboard and mouse you have to look up the controls before starting the game.
The key you were missing was holding left shift to move the vine up (left trigger on a controller), and later left mouse button when controlling two vines at once.
I hope you'll play the game again, since you didn't get to try any of the puzzles!
But thank you for showing interest!