This must be for show. If ByteDance or anyone else is sufficiently motivated to distill OpenAI’s models, it can’t be prevented. You can simply pay other people to collect the data for you.
If you tell someone that they can’t use your product in a certain manner, and then they go to extra lengths to circumvent your measures to gain a profit for themselves, then there is going to be big civil and criminal legal problems.
State sponsored or not; Bytedance has a bank account and business license here in the U.S.
Garbage in = Garbage Out
However, you might wonder what the goal is. This “API distillation” is good for teaching a pretrained model how to do lots of things. But the end result is always constrained by the quality of the pretrained base model, and API outputs don’t help at all with that part.