Not the OP and I must confess that I haven't read anything by Piketty just yet but imho if these are indeed his views then OP seems certainly to be right in saying Picketty only wants that "capitalism should just change some specific things to reduce inequality".
That's also not want Marx really believed in, i.e. he certainly did not believe that we'll all be better off under a different, better form of capitalism. That's what guys like Lassalle [1] believed and what modern European social-democracy really believed too, starting with the 1930s (see the Popular Front in France [2]) up until the 1980s - 1990s (when all modern European social-democracy went into clinical death). Imho the only true heir of Marx that really got to put its hands on the reins of power was Lenin, and it would have been interesting to see how Trotsky would have extended the world revolution outside USSR's borders had be managed to outplay Stalin.