To call someone quixotic is to say that he pursues an ideal with generosity and stubbornness, without measuring what the world answers back, like the gentleman who attacks giants that are windmills. The meaning draws from the book two things it keeps together: the nobility of the purpose and the mismatch with reality.
The gentleman's purpose is noble: he defines for the goatherds the knight-errant as a member of an established order, when times have worsened and malice has grown, to defend maidens, protect widows, and aid orphans. The result is usually bad. He frees galley slaves who stone him, attacks windmills, rescues Andrés from a beating and leaves him to receive a worse one, and always gets thrashed. Hence the use of the adjective for the idealist who fails.
The book complicates the reading. Don Quixote knows what he is doing: when the neighbor tells him he is the honorable gentleman Quijana, he replies "I know who I am," and adds that he may be not only the knights he named, but all the Twelve Peers of France. He confesses to Sancho that he paints Dulcinea in his imagination as he wishes her to be, in beauty and in preeminence. And when they show him the disproof, the enchanter's explanation is already ready. The quixotic, in the book, is less blindness than choice, and this is what Tomé Cecial asks when he wants to know which madman is the madder: the one who is so because he cannot do otherwise, or the one who is so by will.
That is why the adjective carries two meanings. It is praise, for those who do not give up an ideal, and it is reproach, for those who do not see what is before their eyes. Whoever uses it has already chosen one of the classic readings Carpeaux describes, the one that sees in the gentleman's defeat the defeat of faith in a world without faith, or the one that restores the rights of reality.