Saying you’ll do something that’ll harm someone (or, more precisely in this instance, their business) can reasonably be called a threat (in the broad sense of the word), though not necessarily the unfair kind of threat most people imagine when they say ‘threat’.

You can threaten someone with ceasing to be a customer if they don’t change their business practices, and that’s perfectly fine. Sharing publicly available information is generally not a problem, either. But in this case, the author of the message is coming off as very insincere, setting deadlines, and trying to strike up deals, which comes off as unreasonable and makes one wonder if they really are simply going to share publicly available information, or if they’re going to give undue focus over them being ‘uncooperative’. If they did not want their message to come off as a threat, this was very far from an ideal way to write it.