Except that Hillary.com is attempting to intimidate another site into removing its speech. It can remove all the Hildebeasts it wants from its own site. I have no problem there. The free speech issue arises outof its attempt to restrict others.
It would be akin to JimRob telling me I can't post certain info on my personal website because others were lifting it and putting it on FR.
Also, presumably, Hillary.com is a quasi-public site in that it is an advocate for a US Senator.
The problem with your analysis (and say this with the utmost respect for your opinion) is that the so-called free speech dispute is between private parties and as a result the First Amendment to the U.S. Constitution never comes into play. I am absolutely 100% positive that if the parties involved in this dispute were to go to court on the premise that Hillary.com was violating the right of free speech within the constitutional sense, the court would certainly throw the case out and quite possibly impose sanctions against counsel for engaging in frivilous litigation. Also, the conduct of Hillary.com does not equate to "state action" simply because the website is an advocate for a public officer. Both the SCOTUS and the US Court of Appeals for the 2nd Circuit have established a very high threshold for a private organization to be held liable for constitutional violations as if the private person were acting as official arm of a governmental entity. Indeed, I just filed a brief with the US District Court for the SDNY addressing the exact issue. Trust me on this one: Hillary.com can not be held liable for depriving anyone of their First Amendment rights in violation of 42 USCS section 1983.