How does Derek Vinyard get away with only a Manslaughter charge for the "Curb-Stomp"?

Let's take a look at the four/five degrees of murder laws in the United States, shall we?

(summarised from the Wikipedia page)

• First-degree Murder: Intentional, premeditated killing.
• Second-degree Murder: Intentional killing, but not premeditated.
• (Third-degree Murder: Not a thing in most states, including California where the film takes place)
• Voluntary Manslaughter: Intentional killing, not premeditated AND performed under circumstances that can "cause a reasonable person to become emotionally or mentally disturbed"
• Involuntary Manslaughter: Unintentional killing resulting from an intentional or negligent act.

The top and bottom of this list are immediately discarded, Derek Vinyard's actions are a response to people attempting to steal his truck so there is no clear premeditation and he also didn't accidentally put his foot down where somebody was resting their head.

So the distinguishing factor here is whether or not catching the thieves red-handed is ground enough to "cause a reasonable person to become emotionally or mentally disturbed".

Without any further details (e.g. to people who haven't seen the film or the characters in the film making this decision), it would sound pretty reasonable that these are disturbing circumstances that could lead to "cause a reasonable person to become emotionally or mentally disturbed".

Of course, that's really not even close to the whole story. Once the actual curb stomp scene rolls around we know Derek's a huge racist, that he blames other ethnicities for the death of his father (and that the truck they were trying to steal used to be his father's). So it is very much in his best interest (assuming the goal is to minimise his sentence) to accept the voluntary manslaughter charge and not have people dig further. The truth did come out about the actual context, but it was way past the verdict (just before he's up for release).

So, to summarise my answer:

The general shape of the crime matched manslaughter, the details very much matched murder.

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Of course there are narrative and production reasons for him to only receive a short sentence as well. The scenes that take place after he gets out don't need to take place in a visibly later era, the actors don't really need ageing up, etc.

And, definitely intentionally as well, Lamont (who Derek meets in prison and has to spend a lot of time with, and also happens to be black) is in there for six years for assaulting a police officer, illustrating that there is definitely an institutional problem as well.