Yes, the legal language is important. That's why it would have helped a lot if the order either defined "DeepSeek implementations" or said "DeepSeek products or services" in place of "DeepSeek implementations". The order uses different terms, and different terms normally have different meanings.
In particular, footnotes 10 and 13 seem to outright forbid using third-party inference providers of DeepSeek models, and the use of "implementation" there matches a broad meaning of "running a DeepSeek model" in the rest of the order.
It is absolutely clear and unambiguous. "DeekSeek" can only mean the corporate entity "Hangzhou DeepSeek Artificial Intelligence Co., Ltd (DeepSeek)" and so there is no doubt at all about what an "implementation" means in this context.
An implementation must be a third party product that is using a product provided by the DeepSeek corporate entity.