The chairs do have a meaning.
At first we see them straight facing us in the TV. Then they being shifting.
We also see the chair take the place at 1:24 in the whirlwind of petals.
The both of them are also in the chairs later with their broken red strings of fate.

The chairs are meant to symbolize their hearts. At first they were strong and together but then they began to waver. The whirlwind of petals and the chairs meant the whirlwind of feelings and turmoil int heir hearts. For the boy, his indecision piled up (paper planes) while Luka just tossed hers onto the floor not wanting to confront it. She then realizes it's pointless and begins picking up the paper planes and tossing them. Meaning she realizes this indecision in their hearts is unneeded and they are broken. So she leaves. Of course Ａ ＰＡＲＴ ＯＦ ＨＥＲ ＷＩＬＬ ＡＬＷＡＹＳ ＬＯＶＥ ＨＩＭ ＪＵＳＴ ＬＩＫＥ ＨＥ ＷＩＬＬ ＡＬＷＡＹＳ ＬＯＶＥ ＨＥＲ (but they are not *in* love). So her chair remains--her heart remains--with him, with that broken red string of fate.

Heres The Video! [link]