Because he was forced into it
Draco was basically forced to take on the responsibilities of his father, the responsibilities of a Death Eater (which Lucius and Narcissa seemingly did not want for him). Voldemort wished to punish Lucius for his failure to obtain the prophecy from the Department of Mysteries. By giving Draco a task to difficult for him to succeed, Lucius would either have to watch his son die at the hands of the order, or at the hands of Voldemort:
“Draco should be proud,” said Bellatrix indifferently. “The Dark Lord
is granting him a great honor. And I will say this for Draco: He isn’t
shrinking away from his duty, he seems glad of a chance to prove
himself, excited at the prospect —”
Narcissa began to cry in earnest,
gazing beseechingly all the while at Snape.
“That’s because he is
sixteen and has no idea what lies in store! Why, Severus? Why my son?
It is too dangerous! This is vengeance for Lucius’s mistake, I know
Snape said nothing. He looked away from the sight of her tears as
though they were indecent, but he could not pretend not to hear her.
“That’s why he’s chosen Draco, isn’t it?” she persisted. “To punish
Draco believed that if he failed Voldemort in this task, Voldemort would kill him, and his family, to punish them for their failure.
“I haven’t got any options!” said Malfoy, and he was suddenly white as
Dumbledore. “I’ve got to do it! He’ll kill me! He’ll kill my whole
Because he may not have committed many murders or other crimes compared to the other Death Eaters
As far as I can tell, Draco personally killed no one.Voldemort had intended him to kill Dumbledore, or at least attempt to do so, but Snape eventually performed that deed. He did let Death Eaters into the castle, under the threat of violence, and tortured a fellow Death Eater (Rowle), under similar duress. He also used the Imperius curse in another ill-fated attempt to kill Dumbledore, controlling Madame Rosmerta and (indirectly) Katie Bell, as well as employing the crude recourse of poison.
The only individual who died as a result of that first action was Dumbledore, who undoubtedly had been revealed to have planned his death with Snape.
So strictly speaking, Draco may not have killed anyone, and I see no evidence that he ever planned to really follow through on doing so. His first attempts did not end in anyone's death, and not precisely by sheer good fortune but rather by design.
“Oh yes, I do,” said Dumbledore mildly. “You almost killed Katie Bell
and Ronald Weasley. You have been trying, with increasing desperation,
to kill me all year. Forgive me, Draco, but they have been feeble
attempts. . . . So feeble, to be honest, that I wonder whether your
heart has been really in it.”
Draco's first two murder attempts turned out much worse than they should have, if the items had made it to Dumbledore. Dumbledore most likely would have checked his mead for poison, if he cared to drink it at all. Had he received the package, even assuming he would open such an obviously suspicious item, he would certainly have recognized Dark Magic upon it as soon as he opened it. Dumbledore's assessment is likely correct: Draco could not commit himself to any course of action that he really believed would kill Dumbledore.
Yes, he did torture Rowle, but I doubt the Ministry cared about intra-Death-Eater violence. By contrast, virtually all the other Death Eaters seem to have killed at least once.
Because he and his family defected from the Death Eaters (kind of)
Lucius and Narcissa basically gave up on Voldemort by the end.
He saw Ron and Neville bringing down Fenrir Greyback, Aberforth
Stunning Rookwood, Arthur and Percy flooring Thicknesse, and Lucius
and Narcissa Malfoy running through the crowd, not even attempting to
fight, screaming for their son.
So did Draco (by inaction):
Malfoy and Goyle remained slumped hopelessly on the corridor floor;
neither of them had wands. “Let’s stick together. I say we go—Harry,
what’s that on your arm?”
Because the Malfoys had money and power
According to the author,
J.K. Rowling: No, the Malfoys weaseled their way out of trouble
(again) due to the fact that they colluded (albeit out of
self-interest) with Harry at the end of the battle.
Lucius did something similar after the first Wizarding War in Britain.