Trump's point here is that (he believes that) the members of the Democratic party are not behaving in a way so as to support the primary meaning of "democratic", which is
relating to or supporting democracy or its principles.
(definition via GoogleOxford)
Instead, he implies, it is now acting primarily to advance the well-being of its own members.
In other words, he is saying that the Democratic Party is a party for supporting Democrats, not a party for supporting democracy.