European Christendom spent 1095-1291 CE in a futile effort to take the Holy Land from the Infidels and put it back in the hands of Christians. Despite repeated bloodbaths and defeats, Christians persisted for decade after decade, pursuing a failed strategy based on a desire to be "number one" in the Middle East.
Willy Loman likewise clings to a dream, which Happy calls the dream of coming "out number one man." This dream persists because Willy does not know the world has changed and his dream is an illusion. As Biff says, "We've been talking in a dream for fifteen years."
Willy clings to his youthful dream of a salesmen mentor who made deals from his hotel room with his feet up in green velvet slippers. Willy sees the green velvet slippers as the American dream: success falling into your lap while you lounge making sales calls in a room. Willy, always in debt and running to catch up, is now dead tired, even though he never achieved the dream the slippers represent. Still, he can't give up his dream. Willy believes he will achieve material success by being liked and having a winning personality. Willy thinks personality is more important than knowledge or studying. He simply can't abandon the illusion that he will charm his way to success. He needs to believe.
Likewise, the Crusaders, despite repeated defeats, believed God was on their side and would bring them success through military conquest. Neither Willy nor the Crusaders were willing to let reality get in the way. As Biff says of Willy, we might also say of the Crusades: "He [they] had the wrong dreams."
In the end, both dreams end in death: money is ultimately more important to Willy than his life, so he kills himself so his sons can have the insurance money, and to prove to them he is loved by all the people who will show up at his funeral. Aside from Charley, Bernard, and his relatives, no one attends Willy's funeral. Likewise, despite all the killing, God doesn't show the world he is on the Christians' side by giving them the Holy Land.
Willy is more willing to die than he is willing to admit defeat. This is one way that his "quest" resembles a religious crusade.
Rather than accept the end of his career, rather than accept a job with Charley, and rather than celebrate his several accomplishments and talents, Willy instead chooses to kill himself so that his family will be able to collect on his life insurance policy.
Willy is dedicated to an ideal, defined by his brother Ben. Yet this ideal is a delusion, as reinforced by the fact that Ben only appears as a hallucination. The embodiment of Willy's ideal is a ghost; a distortion. The importance of Willy's dream is supreme in his mind because, largely, it is the only measure of success he holds to. It is absolute.
This uncompromising passion also makes his quest like a crusade.