The T cell kills the cancer cell. Some interesting information inside the post
What actually happens is much cooler.
Normal cells are essentially "forced" to provide whatever is inside them to T cells (aka T lymphocytes). It's like being forced to take some of the junk in your house and show it to the police.
If a T cell detects signs of something dangerous (such as a virus), it "orders" normal cells to commit suicide in a way that doesn't spray its contents all over the place and endanger everyone around it (apoptosis). Notice how the cancer cell in the video shrinks instead of bursting.
If you can get T cells to do this intentionally with tumor markers ONLY for cancer, then bam - you've just invented CAR T cell therapy.