This study isn't CAR-T. It is more similar to adoptive TIL therapy because it is using the T cell receptor (TCR) to target the cancer's mutations. This has a huge advantage over CAR-T.
At the moment we use CAR-T to target, mostly, B cell cancers. These cancers have CD19 and CD20 on their cell surface, as do most B cells. We can safely target these cells because it turns out your B cells aren't critical for life. Think of it like an amputation. Your B cells went rogue, you wipe them out.
The problem is this doesn't translate to other cancers, which don't have an obvious cell protein you can target specific to a group of cells you can do without.
All cancer cells have mutations, and all cells in the human body have to display a sample of its proteins on its cell surface. This way our immune system regularly identifies cancer and removes it. Cancers that get established have somehow leveraged local immunosuppression to hold off the immune system, and so the immune system and cancer become a stalemate, or worse the cancer takes off and kills the person.
If we can target the mutations of the cancer, then we can get at the heart of the cancer itself.
You might ask why the cancer just doesn't display it's antigens on the surface. If a cell does this it gets removed by NK cells (natural killers) - our body's fail safe.
What I find interesting is that I didn't think we were close to predicting what TCRs can bind to to a peptide on MHC on the cell surface. I'm going to need to look at the article to findout how they did this. I suspect they used a library of known TCR-antigen interactions.