OK. Your distinction between direct power and direct democracy has been clarified, so I'll set semantic considerations to the side.

I do not see why cyber-libertarianism is incompatible with direct democracy any more than a constitutional republic is. In both cases, basic rights should not (theoretically) be able to be overridden through majority votes. The difference is in what counts as a basic right.

You correctly recognize the key issue that "basic rights" are intrinsically a restriction on democracy. The question is: what counts as "basic rights"? In the U.S., we have a basic set of rights: those enumerated in the Constitution itself plus those that exist as a result of long historical practice plus those recognized by the Supreme Court based on a combination of the other two sources. In a Constitutional republic, rights aren't static, but they're slow to evolve.

Cyber-libertarianism, at least as espoused by many today, embraces a dramatically broader notion of rights. You don't just have the classic rights of Englishmen (life, liberty, and property), but the right to privacy, the right to free and anonymous exchange of information, the right to tinker with your cell phone, the right to turn your apartment into a hotel, the right to transfer money freely and anonymously, etc. Cyber-libertarians tend to believe that government should be restrained from acting unless absolutely necessary, and almost never believe that government action is necessary when it comes to cyberspace. The more rights you recognize, and the broader those rights, the narrower the scope of democratic self determination.

This viewpoint is the diametric opposite of constitutional republicanism. Under that view, government, by the will of the majority, can act so long as it does not invade certain "basic rights." Under cyber-libertarianism, the assumption is reversed. Government is barred from acting unless there is an immensely pressing justification.