Is she recording the live performances as well? Otherwise I don't see a point in including that part on the deal
Her old label are claiming that her singing on tv classifies as a recording (they also banned her from singing her old songs for her televised/streaming concert in China for the same reason).
Looking at various stories from a legal standpoint...technically, it could be seen that way...
...but it's not something that's ever usually enforced as performing old songs on tv would be mutually beneficial, as all parties will make money.
The reason Big Machine are banning her, is clearly as a strong arm tactic to try and force her into signing a contract to agree to not re-record her albums next year (when she is legally allowed to). Same with them refusing the rights for Netflix to use old footage. It's all about trying to pressure her into not re-recording.
It would be smart move... if Swift was likely to give in to their demands...
..but if they think she's going to do that, they haven't been paying attention.